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

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

Edited By Komal Miglani | Updated on Apr 09, 2025 11:48 PM IST

Have you ever wondered what the path of a ball looks like when someone throws a ball in the air? Or have you seen Earth's path when it revolves around the Sun? These are the classic examples of conic sections about which these NCERT notes Class 12 Maths are about. In NCERT Class 11 Maths Chapter 10, students study how the intersection of a plane with a double-napped right circular cone results in different types of curves. The different kinds of curves, viz., circles, ellipses, parabolas, and hyperbolas, have many real-life applications, and students need to build a strong foundation of these concepts to excel in the exam.

This Story also Contains
  1. NCERT Class 11 Chapter 10 Notes
  2. Definition Of A Conic Section (Parabola, Ellipse, And Hyperbola)
  3. Some Important Definitions to Remember
  4. Equation Of A Circle Center (h, k) and Radius r
  5. Standard Forms Of The Equation Of A Parabola
  6. An Equation Of The Ellipse
  7. Equation Of The Hyperbola
  8. Importance of NCERT Class 11 Maths Chapter 11 Notes
  9. NCERT Class 11 Notes Chapter Wise
  10. Subject Wise NCERT Exemplar Solutions
  11. Subject Wise NCERT Solutions
  12. NCERT Books and Syllabus

These class 12 Maths Chapter 10 notes follow the latest CBSE guidelines and contain important concepts and examples. Experienced Careers360 teachers have made these notes, and the step-by-step explanations of the concepts will make learning easier for students. After completing the NCERT textbook exercises, students can use these notes as a revision tool to recall the concepts and formulas. Students can also practice the NCERT Exemplar Class 11 Maths Chapter 11 Conic Section for a better understanding of the chapter. The Class 12 maths NCERT notes PDF has also been provided alongside the article.

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NCERT Class 11 Chapter 10 Notes

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 2nd 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.

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When the plane cuts the cone with a 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.

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

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If α = Ѳ, the section is a parabola.

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If 0 < α < Ѳ, the plane cuts through both sides of the cone, and the curve of intersection is a hyperbola.

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Some Important Definitions to Remember

Axis: The straight line passing through the focus and perpendicular to the directrix is called the axis of the conic section.

Vertex: The point of intersection of the conic section and the axis is called the vertex of the conic section.

Double ordinate: Any chord that is perpendicular to the axis of the conic section is called a double ordinate of the conic section.

Focal chord: Any chord passing through the focus is called the focal chord of the conic section.

Focal distance: The distance between the focus and any point on the conic is known as the focal distance of that point.

Latus rectum: Any chord passing through the focus and perpendicular to the axis is known as the latus rectum of the conic section.

Equation of Conic Section:

The focus at S(h,k) and the Directrix : ax+by+c=0, then equation of conic

PS=ePM(xh)2+(yk)2=e|ax+by+c|a2+b2(xh)2+(yk)2=e2(ax+by+c)2a2+b2

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 the 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 (xh)2+(yk)2, which is the radius of the circle.

Thus, (xh)2+(yk)2=r
Squaring both sides
(xh)2+(yk)2=r2

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Standard Forms Of The Equation Of A Parabola

Parabola:

A parabola is a 2-dimensional plane shape, and it looks like a U shape.

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The distance between P and F is (xa)2+(y0)2
The distance between B and P is (x+a)2+(yy)2
For a parabola, the lengths of PF and BP are equal.
So, (xa)2+(y0)2=(x+a)2+(yy)2
Squaring both sides, we get,
(xa)2+(y0)2=(x+a)2+(yy)2x22ax+y2=x2+2ax+a2y2=4ax
There are four possible cases of the parabola.

Case I

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

The coordinate of the vertex is (0, 0).

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The distance between L and S= the distance of the directrix from the point L.
(xa)2+(y0)2=|x+a12|
Squaring both sides, we get,
(xa)2+y2=(x+a)2x22ax+a2+y2=x2+2ax+a2y2=4ax

Case II

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

The coordinate of the vertex is (0, 0).

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The distance between L and S= the distance of the directrix from the point L
(x+a)2+(y0)2=|xa12|x2+2ax+a2+y2=x22ax+a2y2=4ax

Case III

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

The coordinate of the vertex is (0,0).

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The distance between L and S= the distance of the directrix from the point L.
(x0)2+(ya)2=|y+a12|x2+y22ay+a2=y2+2ay+a2x2=4ay

Case IV

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

The coordinate of the vertex is (0 0).

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The distance between L and S= the distance of the directrix from the point L.
(x0)2+(y+a)2=|ya12|x2+y2+2ay+a2=y22ay+a2x2=4ay

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 coordinates of the endpoints of the major axis are (a,0) and (-a,0) when the major axis is along the x-axis.

Minor Axis: The length of the minor axis is 2b. The coordinates of the endpoints of the major axis are (0,b) and (0,-b) when the minor axis is along 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 e=1b2a2, where 2a is the length of the major axis and 2b is the length of the minor axis.

The eccentricity of an ellipse is less than 1.

The coordinates 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.

Latus rectum: Latus rectum is a line that is parallel to the directrix and passes through a focus. The length of the latus rectum is 2b2a.

The general equation of an ellipse is x2a2+y2b2=1.

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Equation Of The Hyperbola

Hyperbola: A 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 coordinates 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 point 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 coordinates 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 e=1+b2a2, 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 x2a2y2b2=1

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Importance of NCERT Class 11 Maths Chapter 11 Notes

NCERT Class 11 Maths chapter 10 notes are a very competent tool for students who aspire to achieve good marks in the class 11 board exams as well as in other competitive exams. Here are some reasons why students should read these notes.

  • A strong base in conic sections will help students to deal with more complex topics like calculus, geometry and higher Mathematics. These notes will give students that conceptual clarity.
  • These notes contain many images for the better visual representation of the concepts.
  • The latest CBSE 2025-26 guidelines have been followed in these notes.
  • Memorizing these notes will give students better accuracy and speed during solving the questions.
  • These notes are well structured and explained, made by teachers who have multiple years of experience in this field.
  • These notes also contain the previous year’s questions, which students can check to identify common question types.
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Subject Wise NCERT Exemplar Solutions

After completing the NCERT textbooks, students should practice exemplar exercises for a better understanding of the chapters and clarity. The following links will help students to find exemplar exercises.

Subject Wise NCERT Solutions

Students can check the following links for more in-depth learning.

NCERT Books and Syllabus

Students should always check the latest NCERT syllabus before planning their study routine. Also, some reference books should be read after completing the textbook exercises. The following links will be very helpful for students for these purposes.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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