Section Name	Topic Name
11	Conic Sections
11.1	Introduction
11.2	Sections of a Cone
11.3	Circle
11.4	Parabola
11.5	Ellipse
11.6	Hyperbola

National Council of Educational Research and Training (NCERT) Book Solutions for class 11th
Subject: Maths
Chapter: Chapter 11 Conic Sections

Class 11th Maths Chapter 11 Conic Sections NCERT Solution is given below.

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

Question 1:

Ans:

Question 2:

Ans:

 

 

Question 3:

Ans:

Question 4:

Ans:

Question 5:

Ans:

Question 6:

More Resources for CBSE Class 11

• NCERT Solutions
• NCERT Solutions Class 11 Maths
• NCERT Solutions Class 11 Physics
• NCERT Solutions Class 11 Chemistry
• NCERT Solutions Class 11 Biology

Ans:

Question 7:

Ans:

Question 8:

Ans:

Question 9:

Ans:

Question 10:

Ans:

Question 11:

Ans:

Question 12:

Ans:

Question 13:

Ans:


Question 14:

Ans:

Question 15:

Ans:

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

Question 1:

Ans:

Question 2:

Ans:

Question 3:

Ans:

Question 4:

Ans:

Question 5:

Ans:

Question 6:

Ans:

Question 7:

Ans:

Question 8:

Ans:

Question 9:

Ans:

Question 10:

Ans:

Question 11:

Ans:

Question 12:

Ans:

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.3

Question 1:

Ans:

Question 2:

Ans:

Question 3:

Ans:

Question 4:

Ans:

Question 5:

Ans:

Question 6:

Ans:

Question 7:

Ans:

Question 8:

Ans:

Question 9:

Ans:

Question 10:

Ans:

Question 11:

Ans:

Question 12:

Ans:

Question 13:

Ans:

Question 14:

Ans:

Question 15:

Ans:

Question 16:

Ans:

Question 17:

Ans:

Question 18:

Ans:

Question 19:

Ans:

Question 20:

Ans:

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

Question 1:

Ans:

Question 2:

Ans:

Question 3:

Ans:

Question 4:

Ans:

Question 5:

Ans:

Question 6:

Ans:

Question 7:

Ans:

Question 8:

Ans:

Question 9:

Ans:

Question 10:

Ans:

Question 11:

Ans:

Question 12:

Ans:

Question 13:

Ans:

Question 14:

Ans:

Question 15:

Ans:

Class 11 Maths NCERT Solutions – Miscellaneous Questions

Question 1:

Ans:

Question 2:

Ans:


Question 3:

Ans:


Question 4:

Ans:


Question 5:

Ans:

Question 6:

Ans:

Question 7:

Ans:


Question 8:

Ans:

Exercise 11.1 

Q.1: A circle is given with centre (0, 3) and radius 3. Obtain the equation of the given circle.

Q.2: A circle is given with centre (-1, 2) and radius 4. Find the equation of the circle.

Q.4: A circle is given with centre (2, 2) and radius √5

Q.6: The equation of a given circle is given as (a + 5)² + (b – 3)² = 36. Find the centre and radius of the circle.. Obtain the equation of the given circle.

Q.7: The equation of a given circle is given as a² + b² – 4a – 4b + 3 = 0

Find the radius and centre of the circle.

Q.8: The equation of a given circle is given as a² + b² – 6a + 8b – 14 = 0

Find the centre and radius of the circle.

Q.9: The equation of a given circle is given as 2a² + 2b² – 8a = 0

Find the centre and radius of the circle.

Q.10: The circle passing through the points (6, 2) and (4, 3) and whose centre lies on the line 2a + y = 8. Find the equation of the circle.

Q.11: The circle passing through the points (3, 2) and (-2, 2) and whose centre lies on the line a – 3y – 13 = 0. Find the equation of the circle.

Q.12: The radius of the circle is 6 whose centre lies on x – axis and passes through the point (3, 2). Find the equation.

Q.13: The circle passing through (0, 0) and making intercepts a and b on the coordinate axes. Find the equation of the circle.

Q.14: The circle with centre (3, 3) and passes through the point (6, 5), find the equation of a circle?

Q.15: Check whether the point (–2.0, 3.0) lies inside, outside or on the circle x ² + y ² = 25?

Exercise 11.2

Q.1: For the equation y² = 16x, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.2: For the equation x² = 8y, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.3: For the equation y² = – 12x, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.4: For the equation x² = – 20y, determine the focus coordinates,  the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.5: For the equation y² = 24x, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.6: For the equation x² = – 7y, determine the focus coordinates,  the directrix equation, the length of the latus rectum and the axis of the parabola.

Q7. Obtain the equation of the parabola which satisfies the given conditions below:

(i) Focus coordinates = (8, 0)

(ii) Directrix (x) = – 8

Q.8: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Focus coordinates = (0, – 5)

(ii) Directrix (y) = 5

Q.9: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Focus coordinates = (4, 0)

Q.10: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Focus coordinates = (- 3, 0)

Q.11: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Passing through coordinates = (3, 5)

The axis of the parabola is on x – axis.

Q.12: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Passing through coordinates = (6, 4)

The equation is symmetric as considered with y – axis.

Exercise 11.3

Q.7: Obtain the coordinates of the vertices, the foci, the major and the minor axis, the length of the latus rectum and the eccentricity of the ellipse 49x² + 9y² = 441

Q.8: Obtain the coordinates of the vertices, the foci, the major and the minor axis, the length of the latus rectum and the eccentricity of the ellipse 4x² + 16y² = 64

Q.9: Obtain the coordinates of the vertices, the foci, the major and the minor axis, the length of the latus rectum and the eccentricity of the ellipse 4x² + y² = 4

Q.10: For the given condition obtain the equation of the ellipse.

(i) Vertices (±6, 0)

(ii) Foci (±3, 0)

Q.11: For the given condition obtain the equation of the ellipse.

(i) Vertices (0, ±8)

(ii) Foci ( 0, ±4)

Q.12: For the given condition obtain the equation of the ellipse.

(i) Vertices (±5, 0)

(ii) Foci (±3, 0)

Q.13: For the given condition obtain the equation of the ellipse.

(i) Coordinates of major axis (±5, 0)

(ii) Coordinates of minor axis (0, ±3)

Q.14: For the given condition obtain the equation of the ellipse.

(i) Coordinates of major axis (0, ±2)

(ii) Coordinates of minor axis (±√3, 0)

Q.15: For the given condition obtain the equation of the ellipse.

(i) Length of major axis 30

(ii) Coordinates of foci (±4, 0)

Q.16: For the given condition obtain the equation of the ellipse.

(i) Length of minor axis 26

(ii) Coordinates of foci (0, ±9)

Q.17: For the given condition obtain the equation of the ellipse.

(i) Coordinates of foci (±4, 0)

(ii) m = 6

Q.18: For the given condition obtain the equation of the ellipse.

(i) n = 2, c = 3 (on the x – axis)

(ii) Coordinates of centre (0, 0)

Q.19: For the given condition obtain the equation of the ellipse.

(i) Centre is at origin and major axis is along the y – axis

(ii) It passes through the points (1, 6) and (3, 2)

Q.20: For the given condition obtain the equation of the ellipse.

(i) Major axis is represented along x – axis

(ii) It passes through the points (6, 2) and (4, 3)

Exercise 11.4

Q.3: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 25 y² – 4 x² = 100

Q.4: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 9 x² – 4 y² = 36

Q.5: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 6 y² – 16 x² = 96

Q.6: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 64 y² – 9 x² = 96

Q.7: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the vertices (±3, 0)

(ii) Coordinates of the foci (±4, 0)

Q.8: For the given condition obtain the equation of the hyperbola.

 (i) Coordinates of the vertices (0, ±7)

(ii) Coordinates of the foci (0, ±9)

Q.9: For the given condition obtain the equation of the hyperbola.

 (i) Coordinates of the vertices (0, ±8)

(ii) Coordinates of the foci (0, ±11)

Q.10: For the given condition obtain the equation of the hyperbola.

 (i) Coordinates of the foci (±7, 0),

(ii) The length of the transverse axis is 12

Q.11: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (0, ±8)

(ii) The length of the conjugate axis is 16

Q.12: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (±2√3, 0 )

(ii) The length of the latus rectum is 8

Q.13: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (±2√6, 0)

(ii) The length of the latus rectum is 10

Q.15: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (0, ± √10)

(ii) It passes through (2, 3)