Conic Section Class 11th Notes - Free NCERT Class 11 Maths Chapter 11 notes - Download PDF

NCERT Class 11 Maths chapter 11 notes based on the Conic section we will study the Equation of Conic section graph of Conic section, find the general equation of Conic section, tangent, and normal equation. The chapter Conic section Class 11 notes also includes how to draw a Conic section.

Introductory Part may include: The NCERT Class 11 chapter 11 notes Revisiting based on Conic section we will study Equation of Conic section graph of Conic section, find General of Conic section tangent and normal equation of Conic section 10 Notes. CBSE Class 11 Maths chapter 11 notes also cover the basic equations in the chapter. The important terms related to numbers are also covered in the CBSE Class 11 Maths chapter 11 notes. All these topics can be downloaded from Class 11 Maths chapter 11 notes pdf download.

Also, students can refer,

• NCERT Solutions for Class 11 Maths Chapter 11 Conic Section
• NCERT Exemplar Class 11 Maths Chapter 11 Conic Section

NCERT Class 11 Chapter 11 Notes

Conic Section in Two Variables Class 11 Notes- Topic 1:

Definition Of A Conic Section (Parabola, Ellipse, And Hyperbola)

A Conic section is the locus of a point in a plane so that its distance from a fixed point in the plane bears a constant ratio to its distance from a fixed line. The fixed point is called the focus of the Conic section and the constant distance is called the directrix.

The Conic section can be obtained as sections of a right circular cone by a plane in various positions and that is why they are called conic sections. A conic is given by a 2ed degree equation. Thus a conic means a pair of straight lines, a circle, a parabola, an ellipse, or a hyperbola. A circle is a limiting case of an ellipse.

When the plane cuts the cone with semi-vertical angle Ѳ at an angle α with the vertical axis of the cone we have the following:

If α = 90°, the section is a circle

If Ѳ < α < 90°, the section is an ellipse

If α = Ѳ, the section is a parabola

If 0 < α < Ѳ,

the plane cuts through both the sides of the cone, and the curve of intersection is a hyperbola.

Equation Of A Conic Section

Let the focus of the conic be (α, β) and the directrix be the line ax + by + c = 0, e being the eccentricity, then equation of the conic is the locus of the point P (h, k), such that

Equation Of A Circle Center (h, k) And Radius r

Circle:

The distance of any point on the circumference of the circle from the center is always constant and the distance is known as radius.

Assume that (h,k) be the radius of the circle, (x,y) be any point on the circumference of the circle, and r be the radius of the circle.

The distance between (h,k) and (x,y) is which is the radius of the circle.

Thus,

Squaring both sides

Standard Forms Of The Equation Of A Parabola

Parabola:

Parabola is a 2-dimensional plane shape and it looks like a U shape.

The distance between P and F is

The distance between B and P is

For parabola the length of PF and BP are equal.

So,

Squaring both sides

There are four cases is possible of the parabola

Case I

The axis of the parabola along x-axis and the equation of directrix is x+a = 0

The co-ordinate of the vertex is (0,0)

The distance between L and S = the distance of the directrix from the point L

Squaring both sides

Case II

The axis of the parabola along x axis and the equation of directrix is x-a = 0.

Coordinate of the vertex is (0,0)

The distance between L and S = the distance of the directrix from the point L

Case III

The axis of the parabola along y axis and the equation of directrix is y+a = 0.

Coordinate of the vertex is (0,0).

The distance between L and S = the distance of the directrix from the point L

Case IV

The axis of the parabola along y axis and the equation of directrix is y-a = 0.

Coordinate of the vertex is (0 0)

The distance between L and S = the distance of the directrix from the point L

An Equation Of The Ellipse

Ellipse: It is a 2-dimensional shape in a plane. It has two foci and two directrices.

Major Axis: The length of the major axis is 2a. The coordinate of endpoints of the major axis is (a,0) and (-a,0) when the major axis is along x-axis.

Minor Axis: The length of the minor axis is 2b. The coordinate of endpoints of the major axis is (0,b) and (0,-b) when the minor axis is along y-axis.

Eccentricity: The ratio of the distance of the focus from the center of the ellipse, and the distance of one end of the ellipse from the center of the ellipse. It is denoted by e.

The value of, where 2a is the length of the major axis and 2b is the length of the minor axis.

The eccentricity for an ellipse is less than 1.

The coordinate of foci are (-ae,0) and (ae,0) where the major axis is along the x-axis, and the minor axis is the y-axis.

Latus rectum: Latus rectum is a line that is parallel with directrix and passes through a focus. The length of the latus rectum is

The general equation of an ellipse is

Equation Of The Hyperbola

Hyperbola: Hyperbola is a 2-dimensional shape. A hyperbola has two foci and two directrices.

Major Axis: The length of the major axis is 2a.

Minor Axis: The length of the minor axis is 2b.

Vertex: A hyperbola has two vertices and the coordinate of the vertices are (a,0) and (-a,0) when the major axis is along the x-axis.

Focus: The distance of any point on the hyperbola from a fixed on the major axis and the distance of that of the hyperbola and directrix are always constant. The fixed point is known as focus. The coordinate of the foci are (-ae,0) and (ae,0) where the major axis is along the x-axis, and the minor axis is the y-axis.

Eccentricity: The ratio of the distance of the focus from the center of the ellipse, and the distance of one end of the ellipse from the center of the ellipse. It is denoted by e.

The value of where 2a is the length of the major axis and 2b is the length of the minor axis. The eccentricity of a hyperbola is always greater than 1.

The general equation of a hyperbola is

Significance of NCERT Class 11 Maths Chapter 11 Notes

Conic section Class 11 Notes is helpful to revise the chapter and to study the main topics covered in the chapter. Also, this NCERT Class 11 Maths chapter 11 is useful to understand the topics of Class 11 CBSE Maths Syllabus. CBSE Class 11 Maths chapter 11 notes help to understand the concept of numbers. These notes can also be downloaded from Conic section Class 11 notes pdf download. Class 11 Conic section contains the Conic section. We will study the Equation of Conic section graph of Conic section, find radii of Conic section tangent and normal equation.

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