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NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections are provided here. As the name suggests a conic section is a curve obtained from the intersection of the surface of a cone with a plane. There are three types of conic section hyperbola, the parabola, and the ellipse discussed in the Class 11 NCERT syllabus. The circle is a special case of the ellipse which has been discussed in this class 11 maths NCERT book chapter. In the conic sections class 11 questions and answers, you will see problems related to above-mentioned curves like circles, parabolas, hyperbolas and ellipses. These NCERT solutions are developed by expert team of Careers360 based on the latest syllabus of CSBE 2023. In the class 11 maths chapter 11 question answer, you will get solutions to miscellaneous exercise too. Here students can find NCERT solutions for class 11 at single place.
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The CBSE syllabus features of conic sections class 11, which covers key topics including Conic Sections, Sections of a Circle, as well as Circle, Parabola, Hyperbola, and Ellipse. these concepts are essential for both CBSE exam and competitive exams like JEE Mains, JEE Advanced, VITEEE, BITSAT etc because every year many questions are asked from this topic. There is a total of 62 questions are given in 4 exercises of NCERT textbook. All these questions are explained in the class 11 maths chapter 11 NCERT solutions. These curves have applications in fields like the design of antennas and telescopes, planetary motion, reflectors in automobile headlights, etc. There are 8 questions in a miscellaneous exercise.
Also Read| Conic Section Class 11 Maths Chapter Notes
Also Read| NCERT Exemplar Solutions For Class 11 Maths Chapter Conic Sections
Circle:
Description | Equation/Formulas |
Equation of a circle | (x - h)2 + (y - k)2 = r2 |
General equation of a circle | x2 + y2 + 2gx + 2fy + c = 0 |
Center of the circle | Centre: (-g, -f) |
Radius of the circle | Radius (r) = √(g2 + f2 - c) |
Parametric equation of a circle | x = r cos(θ), y = r sin(θ) |
Parametric equation of a circle (centred at h, k) | x = h + r cos(θ), y = k + r sin(θ) |
Parabola:
Description | Equations/Forms |
Equation forms of parabola | y2 = 4ax, y2 = -4ax, x2 = 4ay, x2 = -4ay |
Axis of the parabola | y = 0 (for first two forms), x = 0 (for last two forms) |
Directrix of the parabola | x = -a (1st form), x = a (2nd form), y = -a (3rd form), y = a (4th form) |
Vertex of the parabola | (0, 0) (for all forms) |
Focus of the parabola | (a, 0) (1st form), (-a, 0) (2nd form), (0, a) (3rd form), (0, -a) (4th form) |
Length of latus rectum | 4a (for all forms) |
Focal length | ` |
Ellipse:
Description | Equation/Forms |
Equation forms of ellipse | x2/a2 + y2/b2 = 1 (a > b), x2/b2 + y2/a2 = 1 (a > b) |
Major Axis | y = 0 (1st form), x = 0 (2nd form) |
Length of Major Axis | 2a (for both forms) |
Minor Axis | x = 0 (1st form), y = 0 (2nd form) |
Length of Minor Axis | 2b (for both forms) |
Directrix of the ellipse | x = ±a/e (1st form), y = ±a/e (2nd form) |
Vertex of the ellipse | (±a, 0) (1st form), (0, ±a) (2nd form) |
Focus of the ellipse | (±ae, 0) (1st form), (0, ±ae) (2nd form) |
Length of latus rectum | 2b2/a (for both forms) |
Eccentricity (e) | √(a2 + b2)/a2 (for both forms) |
conic sections class 11 questions and answers
Description | Equations/Forms |
Equation forms of hyperbola | x2/a2 - y2/b2 = 1, x2/a2 - y2/b2 = -1 |
Coordinates of centre | (0, 0) (for both forms) |
Coordinates of vertices | (±a, 0) (for both forms) |
Coordinates of foci | (±ae, 0) (for both forms) |
Length of Conjugate axis | 2b (for both forms) |
Length of Transverse axis | 2a (for both forms) |
Equation of Conjugate axis | x = 0 (for both forms) |
Equation of Transverse axis | y = 0 (for both forms) |
Equation of Directrix | x = ±a/e (for both forms) |
Eccentricity (e) | √(a2 + b2)/a2 (for both forms) |
Length of latus rectum | 2b2/a (for both forms) |
Free download NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections for CBSE Exam.
NCERT conic sections class 11 solutions - Exercise: 11.1
Question:1 Find the equation of the circle with
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
So Given Here
AND
So the equation of the circle is:
,
Question:2 Find the equation of the circle with
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
So Given Here
AND
So the equation of the circle is:
,
Question:3 Find the equation of the circle with
Answer:
As we know,
The equation of the circle with center ( h, k) and radius r is give by ;
So Given Here
AND
So the equation of circle is:
,
Question:4 Find the equation of the circle with
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
So Given Here
AND
So the equation of the circle is:
,
Question:5 Find the equation of the circle with
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
So Given Here
AND
So the equation of the circle is:
,
Question:6 Find the centre and radius of the circles.
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Given here
Can also be written in the form
So, from comparing, we can see that
Hence the Radius of the circle is 6.
Question:7 Find the centre and radius of the circles.
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Given here
Can also be written in the form
So, from comparing, we can see that
Hence the Radius of the circle is .
Question:8 Find the centre and radius of the circles.
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Given here
Can also be written in the form
So, from comparing, we can see that
Hence the radius of the circle is .
Question:9 Find the centre and radius of the circles.
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Given here
Can also be written in the form
So, from comparing, we can see that
Hence Center of the circle is the Radius of the circle is .
Question:10 Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line .
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Given Here,
Condition 1: the circle passes through points (4,1) and (6,5)
Here,
Now, Condition 2:centre is on the line .
From condition 1 and condition 2
Now lets substitute this value of h and k in condition 1 to find out r
So now, the Final Equation of the circle is
Question:11 Find the equation of the circle passing through the points (2,3) and (–1,1) and hose centre is on the line .
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
Given Here,
Condition 1: the circle passes through points (2,3) and (–1,1)
Here,
Now, Condition 2: centre is on the line.
From condition 1 and condition 2
Now let's substitute this value of h and k in condition 1 to find out
So now, the Final Equation of the circle is
Answer:
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
So let the circle be,
Since it's radius is 5 and its centre lies on x-axis,
And Since it passes through the point (2,3).
When ,The equation of the circle is :
When The equation of the circle is :
Question:13 Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.
Answer:
Let the equation of circle be,
Now since this circle passes through (0,0)
Now, this circle makes an intercept of a and b on the coordinate axes.it means circle passes through the point (a,0) and (0,b)
So,
Since
Similarly,
Since b is not equal to zero.
So Final equation of the Circle ;
Question:14 Find the equation of a circle with centre (2,2) and passes through the point (4,5).
Answer:
Let the equation of circle be :
Now, since the centre of the circle is (2,2), our equation becomes
Now, Since this passes through the point (4,5)
Hence The Final equation of the circle becomes
Question:15 Does the point (–2.5, 3.5) lie inside, outside or on the circle ?
Answer:
Given, a circle
As we can see center of the circle is ( 0,0)
Now the distance between (0,0) and (–2.5, 3.5) is
Since distance between the given point and center of the circle is less than radius of the circle, the point lie inside the circle.
Conic sections class 11 NCERT solutions - Exercise: 11.2
Answer:
Given, a parabola with equation
This is parabola of the form which opens towards the right.
So,
By comparing the given parabola equation with the standard equation, we get,
Hence,
Coordinates of the focus :
Axis of the parabola:
It can be seen that the axis of this parabola is X-Axis.
The equation of the directrix
The length of the latus rectum:
.
Answer:
Given, a parabola with equation
This is parabola of the form which opens upward.
So,
By comparing the given parabola equation with the standard equation, we get,
Hence,
Coordinates of the focus :
Axis of the parabola:
It can be seen that the axis of this parabola is Y-Axis.
The equation of the directrix
The length of the latus rectum:
.
Answer:
Given, a parabola with equation
This is parabola of the form which opens towards left.
So,
By comparing the given parabola equation with the standard equation, we get,
Hence,
Coordinates of the focus :
Axis of the parabola:
It can be seen that the axis of this parabola is X-Axis.
The equation of the directrix
The length of the latus rectum:
.
Answer:
Given, a parabola with equation
This is parabola of the form which opens downwards.
So,
By comparing the given parabola equation with the standard equation, we get,
Hence,
Coordinates of the focus :
Axis of the parabola:
It can be seen that the axis of this parabola is Y-Axis.
The equation of the directrix
The length of the latus rectum:
.
Answer:
Given, a parabola with equation
This is parabola of the form which opens towards the right.
So,
By comparing the given parabola equation with the standard equation, we get,
Hence,
Coordinates of the focus :
Axis of the parabola:
It can be seen that the axis of this parabola is X-Axis.
The equation of the directrix
The length of the latus rectum:
.
Answer:
Given, a parabola with equation
This is parabola of the form which opens downwards.
So
By comparing the given parabola equation with the standard equation, we get,
Hence,
Coordinates of the focus :
Axis of the parabola:
It can be seen that the axis of this parabola is Y-Axis.
The equation of the directrix
The length of the latus rectum:
.
Question:7 Find the equation of the parabola that satisfies the given conditions:
Answer:
Given, in a parabola,
Focus : (6,0) And Directrix :
Here,
Focus is of the form (a, 0), which means it lies on the X-axis. And Directrix is of the form which means it lies left to the Y-Axis.
These are the condition when the standard equation of a parabola is.
Hence the Equation of Parabola is
Here, it can be seen that:
Hence the Equation of the Parabola is:
.
Question:8 Find the equation of the parabola that satisfies the given conditions:
Answer:
Given,in a parabola,
Focus : Focus (0,–3); directrix
Here,
Focus is of the form (0,-a), which means it lies on the Y-axis. And Directrix is of the form which means it lies above X-Axis.
These are the conditions when the standard equation of a parabola is .
Hence the Equation of Parabola is
Here, it can be seen that:
Hence the Equation of the Parabola is:
.
Question:9 Find the equation of the parabola that satisfies the given conditions:
Answer:
Given,
Vertex (0,0) And focus (3,0)
As vertex of the parabola is (0,0) and focus lies in the positive X-axis, The parabola will open towards the right, And the standard equation of such parabola is
Here it can be seen that
So, the equation of a parabola is
.
Question:10 Find the equation of the parabola that satisfies the given conditions:
Answer:
Given,
Vertex (0,0) And focus (-2,0)
As vertex of the parabola is (0,0) and focus lies in the negative X-axis, The parabola will open towards left, And the standard equation of such parabola is
Here it can be seen that
So, the equation of a parabola is
.
Question:11 Find the equation of the parabola that satisfies the given conditions:
Vertex (0,0) passing through (2,3) and axis is along x -axis.
Answer:
Given
The Vertex of the parabola is (0,0).
The parabola is passing through (2,3) and axis is along the x -axis, it will open towards right. and the standard equation of such parabola is
Now since it passes through (2,3)
So the Equation of Parabola is ;
Question:12 Find the equation of the parabola that satisfies the given conditions:
Vertex (0,0), passing through (5,2) and symmetric with respect to y -axis.
Answer:
Given a parabola,
with Vertex (0,0), passing through (5,2) and symmetric with respect to the y -axis.
Since the parabola is symmetric with respect to Y=axis, it's axis will ve Y-axis. and since it passes through the point (5,2), it must go through the first quadrant.
So the standard equation of such parabola is
Now since this parabola is passing through (5,2)
Hence the equation of the parabola is
NCERT class 11 maths chapter 11 question answer - Exercise: 11.3
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along X-axis and the minor axis is along Y-axis.
On comparing the given equation with the standard equation of an ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along Y-axis and the minor axis is along X-axis.
On comparing the given equation with the standard equation of such ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along X-axis and the minor axis is along Y-axis.
On comparing the given equation with the standard equation of an ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along Y-axis and the minor axis is along X-axis.
On comparing the given equation with the standard equation of such ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of ellipse
As we can see from the equation, the major axis is along X-axis and the minor axis is along Y-axis.
On comparing the given equation with standard equation of ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along Y-axis and the minor axis is along X-axis.
On comparing the given equation with the standard equation of such ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along Y-axis and the minor axis is along X-axis.
On comparing the given equation with the standard equation of such ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along Y-axis and the minor axis is along X-axis.
On comparing the given equation with the standard equation of such ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Answer:
Given
The equation of the ellipse
As we can see from the equation, the major axis is along X-axis and the minor axis is along Y-axis.
On comparing the given equation with the standard equation of an ellipse, which is
We get
and .
So,
Hence,
Coordinates of the foci:
The vertices:
The length of the major axis:
The length of minor axis:
The eccentricity :
The length of the latus rectum:
Question:10 Find the equation for the ellipse that satisfies the given conditions:
Vertices (± 5, 0), foci (± 4, 0)
Answer:
Given, In an ellipse,
Vertices (± 5, 0), foci (± 4, 0)
Here Vertices and focus of the ellipse are in X-axis so the major axis of this ellipse will be X-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( vertices and foci) with the given one, we get
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:11 Find the equation for the ellipse that satisfies the given conditions:
Vertices (0, ± 13), foci (0, ± 5)
Answer:
Given, In an ellipse,
Vertices (0, ± 13), foci (0, ± 5)
Here Vertices and focus of the ellipse are in Y-axis so the major axis of this ellipse will be Y-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( vertices and foci) with the given one, we get
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:12 Find the equation for the ellipse that satisfies the given conditions:
Vertices (± 6, 0), foci (± 4, 0)
Answer:
Given, In an ellipse,
Vertices (± 6, 0), foci (± 4, 0)
Here Vertices and focus of the ellipse are in X-axis so the major axis of this ellipse will be X-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( vertices and foci) with the given one, we get
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:13 Find the equation for the ellipse that satisfies the given conditions:
Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)
Answer:
Given, In an ellipse,
Ends of the major axis (± 3, 0), ends of minor axis (0, ± 2)
Here, the major axis of this ellipse will be X-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( ends of the major and minor axis ) with the given one, we get
and
Hence, The Equation of the ellipse will be :
Which is
.
Question:14 Find the equation for the ellipse that satisfies the given conditions:
Ends of major axis (0, ± ), ends of minor axis (± 1, 0)
Answer:
Given, In an ellipse,
Ends of the major axis (0, ± ), ends of minor axis (± 1, 0)
Here, the major axis of this ellipse will be Y-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( ends of the major and minor axis ) with the given one, we get
and
Hence, The Equation of the ellipse will be :
Which is
.
Question:15 Find the equation for the ellipse that satisfies the given conditions:
Length of major axis 26, foci (± 5, 0)
Answer:
Given, In an ellipse,
Length of major axis 26, foci (± 5, 0)
Here, the focus of the ellipse is in X-axis so the major axis of this ellipse will be X-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( Length of semimajor axis and foci) with the given one, we get
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:16 Find the equation for the ellipse that satisfies the given conditions:
Length of minor axis 16, foci (0, ± 6).
Answer:
Given, In an ellipse,
Length of minor axis 16, foci (0, ± 6).
Here, the focus of the ellipse is on the Y-axis so the major axis of this ellipse will be Y-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( length of semi-minor axis and foci) with the given one, we get
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:17 Find the equation for the ellipse that satisfies the given conditions:
Answer:
Given, In an ellipse,
V Foci (± 3, 0), a = 4
Here foci of the ellipse are in X-axis so the major axis of this ellipse will be X-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
So on comparing standard parameters( vertices and foci) with the given one, we get
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:18 Find the equation for the ellipse that satisfies the given conditions:
b = 3, c = 4, centre at the origin; foci on the x axis.
Answer:
Given,In an ellipse,
b = 3, c = 4, centre at the origin; foci on the x axis.
Here foci of the ellipse are in X-axis so the major axis of this ellipse will be X-axis.
Therefore, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
Also Given,
and
Now, As we know the relation,
Hence, The Equation of the ellipse will be :
Which is
.
Question:19 Find the equation for the ellipse that satisfies the given conditions:
Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).
Answer:
Given,in an ellipse
Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).
Since, The major axis of this ellipse is on the Y-axis, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
Now since the ellipse passes through points,(3, 2)
since the ellipse also passes through points,(1, 6).
On solving these two equation we get
and
Thus, The equation of the ellipse will be
.
Question:20 Find the equation for the ellipse that satisfies the given conditions:
Major axis on the x-axis and passes through the points (4,3) and (6,2) .
Answer:
Given, in an ellipse
Major axis on the x-axis and passes through the points (4,3) and (6,2).
Since The major axis of this ellipse is on the X-axis, the equation of the ellipse will be of the form:
Where and are the length of the semimajor axis and semiminor axis respectively.
Now since the ellipse passes through the point,(4,3)
since the ellipse also passes through the point (6,2).
On solving this two equation we get
and
Thus, The equation of the ellipse will be
NCERT class 11 maths chapter 11 question answer - Exercise: 11.4
Answer:
Given a Hyperbola equation,
Can also be written as
Comparing this equation with the standard equation of the hyperbola:
We get,
and
Now, As we know the relation in a hyperbola,
Here as we can see from the equation that the axis of the hyperbola is X -axis. So,
Coordinates of the foci:
The Coordinates of vertices:
The Eccentricity:
The Length of the latus rectum :
Question:2 Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.
Answer:
Given a Hyperbola equation,
Can also be written as
Comparing this equation with the standard equation of the hyperbola:
We get,
and
Now, As we know the relation in a hyperbola,
Here as we can see from the equation that the axis of the hyperbola is Y-axis. So,
Coordinates of the foci:
The Coordinates of vertices:
The Eccentricity:
The Length of the latus rectum :
Answer:
Given a Hyperbola equation,
Can also be written as
Comparing this equation with the standard equation of the hyperbola:
We get,
and
Now, As we know the relation in a hyperbola,
Hence,
Coordinates of the foci:
The Coordinates of vertices:
The Eccentricity:
The Length of the latus rectum :
Answer:
Given a Hyperbola equation,
Can also be written as
Comparing this equation with the standard equation of the hyperbola:
We get,
and
Now, As we know the relation in a hyperbola,
Therefore,
Coordinates of the foci:
The Coordinates of vertices:
The Eccentricity:
The Length of the latus rectum :
Answer:
Given a Hyperbola equation,
Can also be written as
Comparing this equation with the standard equation of the hyperbola:
We get,
and
Now, As we know the relation in a hyperbola,
Here as we can see from the equation that the axis of the hyperbola is Y-axis. So,
Coordinates of the foci:
The Coordinates of vertices:
The Eccentricity:
The Length of the latus rectum :
Answer:
Given a Hyperbola equation,
Can also be written as
Comparing this equation with the standard equation of the hyperbola:
We get,
and
Now, As we know the relation in a hyperbola,
Therefore,
Coordinates of the foci:
The Coordinates of vertices:
The Eccentricity:
The Length of the latus rectum :
Question:7 Find the equations of the hyperbola satisfying the given conditions.
Vertices (± 2, 0), foci (± 3, 0)
Answer:
Given, in a hyperbola
Vertices (± 2, 0), foci (± 3, 0)
Here, Vertices and focii are on the X-axis so, the standard equation of the Hyperbola will be ;
By comparing the standard parameter (Vertices and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Hence,The Equation of the hyperbola is ;
Question:8 Find the equations of the hyperbola satisfying the given conditions.
Vertices (0, ± 5), foci (0, ± 8)
Answer:
Given, in a hyperbola
Vertices (0, ± 5), foci (0, ± 8)
Here, Vertices and focii are on the Y-axis so, the standard equation of the Hyperbola will be ;
By comparing the standard parameter (Vertices and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Hence, The Equation of the hyperbola is ;
.
Question:9 Find the equations of the hyperbola satisfying the given conditions.
Vertices (0, ± 3), foci (0, ± 5)
Answer:
Given, in a hyperbola
Vertices (0, ± 3), foci (0, ± 5)
Here, Vertices and focii are on the Y-axis so, the standard equation of the Hyperbola will be ;
By comparing the standard parameter (Vertices and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Hence, The Equation of the hyperbola is ;
.
Question:10 Find the equations of the hyperbola satisfying the given conditions.
Foci (± 5, 0), the transverse axis is of length 8.
Answer:
Given, in a hyperbola
Foci (± 5, 0), the transverse axis is of length 8.
Here, focii are on the X-axis so, the standard equation of the Hyperbola will be ;
By comparing the standard parameter (transverse axis length and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Hence, The Equation of the hyperbola is ;
Question:11 Find the equations of the hyperbola satisfying the given conditions.
Foci (0, ±13), the conjugate axis is of length 24.
Answer:
Given, in a hyperbola
Foci (0, ±13), the conjugate axis is of length 24.
Here, focii are on the Y-axis so, the standard equation of the Hyperbola will be ;
By comparing the standard parameter (length of conjugate axis and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Hence, The Equation of the hyperbola is ;
.
Question:12 Find the equations of the hyperbola satisfying the given conditions.
Foci , the latus rectum is of length 8 .
Answer:
Given, in a hyperbola
Foci , the latus rectum is of length 8.
Here, focii are on the X-axis so, the standard equation of the Hyperbola will be ;
By comparing standard parameter (length of latus rectum and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Since can never be negative,
Hence, The Equation of the hyperbola is ;
Question:13 Find the equations of the hyperbola satisfying the given conditions.
Foci (± 4, 0), the latus rectum is of length 12
Answer:
Given, in a hyperbola
Foci (± 4, 0), the latus rectum is of length 12
Here, focii are on the X-axis so, the standard equation of the Hyperbola will be ;
By comparing standard parameter (length of latus rectum and foci) with the given one, we get
and
Now, As we know the relation in a hyperbola
Since can never be negative,
Hence, The Equation of the hyperbola is ;
Question:14 Find the equations of the hyperbola satisfying the given conditions.
Answer:
Given, in a hyperbola
vertices (± 7,0), And
Here, Vertices is on the X-axis so, the standard equation of the Hyperbola will be ;
By comparing the standard parameter (Vertices and eccentricity) with the given one, we get
and
From here,
Now, As we know the relation in a hyperbola
Hence, The Equation of the hyperbola is ;
Question:15 Find the equations of the hyperbola satisfying the given conditions.
Answer:
Given, in a hyperbola,
Foci , passing through (2,3)
Since foci of the hyperbola are in Y-axis, the equation of the hyperbola will be of the form ;
By comparing standard parameter (foci) with the given one, we get
Now As we know, in a hyperbola
Now As the hyperbola passes through the point (2,3)
Solving Equation (1) and (2)
Now, as we know that in a hyperbola is always greater than, we choose the value
Hence The Equation of the hyperbola is
Class 11 maths chapter 11 NCERT solutions - Miscellaneous Exercise
Question:1 If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
Answer:
Le the parabolic reflector opens towards the right.
So the equation of parabolic reflector will be,
Now, Since this curve will pass through the point (5,10) if we assume origin at the optical centre,
So
Hence, The focus of the parabola is,
.
Alternative Method,
As we know on any concave curve
Hence, Focus
.
Hence the focus is 5 cm right to the optical centre.
Answer:
Since the Axis of the parabola is vertical, Let the equation of the parabola be,
it can be seen that this curve will pass through the point (5/2, 10) if we assume origin at the bottom end of the parabolic arch.
So,
Hence, the equation of the parabola is
Now, when y = 2 the value of x will be
Hence the width of the arch at this height is
Answer:
Given,
The width of the parabolic cable = 100m
The length of the shorter supportive wire attached = 6m
The length of the longer supportive wire attached = 30m
Since the rope opens towards upwards, the equation will be of the form
Now if we consider origin at the centre of the rope, the equation of the curve will pass through points, (50,30-6)=(50,24)
Hence the equation of the parabola is
Now at a point, 18 m right from the centre of the rope, the x coordinate of that point will be 18, so by the equation, the y-coordinate will be
Hence the length of the supporting wire attached to roadway from the middle is 3.11+6=9.11m.
Answer:
The equation of the semi-ellipse will be of the form
Now, According to the question,
the length of major axis = 2a = 8
The length of the semimajor axis =2
Hence the equation will be,
Now, at point 1.5 cm from the end, the x coordinate is 4-1.5 = 2.5
So, the height at this point is
Hence the height of the required point is 1.56 m.
Answer:
Let be the angle that rod makes with the ground,
Now, at a point 3 cm from the end,
At the point touching the ground
Now, As we know the trigonometric identity,
Hence the equation is,
Answer:
Given the parabola,
Comparing this equation with , we get
Now, As we know the coordinates of ends of latus rectum are:
So, the coordinates of latus rectum are,
Now the area of the triangle with coordinates (0,0),(6,3) and (-6,3)
Widht of the triangle = 2*6=12
Height of the triangle = 3
So The area =
Hence the required area is 18 unit square.
Answer:
As we know that if a point moves in a plane in such a way that its distance from two-point remain constant then the path is an ellipse.
Now, According to the question,
the distance between the point from where the sum of the distance from a point is constant = 10
Now, the distance between the foci=8
Now, As we know the relation,
Hence the equation of the ellipse is,
Hence the path of the man will be
Answer:
Given, an equilateral triangle inscribed in parabola with the equation.
The one coordinate of the triangle is A(0,0).
Now, let the other two coordinates of the triangle are
and
Now, Since the triangle is equilateral,
The coordinates of the points of the equilateral triangle are,
So, the side of the triangle is
11.2 Sections of a Cone
11.3 Circle
11.4 Parabola
11.5 Ellipse
11.6 Hyperbola
Interested students can practice class 11 maths ch 11 question answer using the exercises listed below.
chapter-1 | Sets |
chapter-2 | Relations and Functions |
chapter-3 | Trigonometric Functions |
chapter-4 | Principle of Mathematical Induction |
chapter-5 | Complex Numbers and Quadratic equations |
chapter-6 | Linear Inequalities |
chapter-7 | Permutation and Combinations |
chapter-8 | Binomial Theorem |
chapter-9 | Sequences and Series |
chapter-10 | Straight Lines |
chapter-11 | Conic Section |
chapter-12 | Introduction to Three Dimensional Geometry |
chapter-13 | Limits and Derivatives |
chapter-14 | Mathematical Reasoning |
chapter-15 | Statistics |
chapter-16 | Probability |
Easy Solutions: NCERT Solutions of ch 11 maths class 11 provide step-by-step solutions to all the questions in the textbook. These solutions are easy to understand and follow, making it easier for students to learn.
Simple Language: The language used in the textbook and chapter 11 class 11 maths solutions is simple and easy to comprehend. This helps students to grasp the concepts better and avoid confusion.
Extensive Coverage: The class 11 chapter 11 maths covers all the essential topics related to Conic Sections, such as the properties and equations of Circle, Parabola, Hyperbola, and Ellipse. This comprehensive coverage enables students to gain a deep understanding of the subject matter.
Tip- You should remember standard equations and formulas for all the standard curves and try to solve problems from NCERT including miscellaneous exercise. If you are not able to do, you can take help from the NCERT solutions for class 11 maths chapter 11 conic section.
Happy Reading !!!
Conic sections class 11 solutions encompass significant topics that enhance understanding of concepts such as ellipse, hyperbola, and more. The introductory portion of this chapter offers students an overall understanding of the basics that are crucial for board exams. Subsequent sections elaborate on elements like standard equations of parabola, degenerate conic sections, latus rectum, and ellipse.
Class 11 maths conic sections holds significant importance in Class 11 Mathematics. After students have covered the fundamental areas, they can tackle the exercise problems with greater ease. By solving problems pertaining to this chapter, students can sharpen their analytical and logical thinking abilities. Selecting appropriate study materials is also crucial for scoring well in Class 11 exams, including the board exams. The primary objective of developing NCERT Solutions is to assist students in identifying the concepts in which they need improvement and guiding them to achieve better scores.
Accuracy is crucial in Mathematics, and consistent practice is essential to achieve it. With numerous study materials available online, selecting the right one can be a daunting task. By choosing solutions that concentrate solely on the CBSE Syllabus, students can comprehend the crucial concepts that are significant from an examination perspective. Class 11th conic section solution provided by Careers360 team are includes all these points.
Students can get the detailed NCERT solutions for class 11 maths by clicking on the link. students can practice these solutions to get indepth understanding of concepts.
Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.
The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.
A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.
GIS officer work on various GIS software to conduct a study and gather spatial and non-spatial information. GIS experts update the GIS data and maintain it. The databases include aerial or satellite imagery, latitudinal and longitudinal coordinates, and manually digitized images of maps. In a career as GIS expert, one is responsible for creating online and mobile maps.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.
If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi.
Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.
Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.
Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.
Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.
A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.
A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.
Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.
Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.
A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.
Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.
The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.
An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.
Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.
For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.
An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.
They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.
Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.