# NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

Topics and Sub Topics in Class 11 Maths Chapter 11 Conic Sections:

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

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**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

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### NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

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### NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.3

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### NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

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### Class 11 Maths NCERT Solutions – Miscellaneous Questions

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**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 a ^{2 }+ b^{2} – 4a – 4b + 3 = 0**

**Find the radius and centre of the circle.**

**Q.8: The equation of a given circle is given as a ^{2 }+ b^{2} – 6a + 8b – 14 = 0**

**Find the centre and radius of the circle.**

**Q.9: The equation of a given circle is given as 2a ^{2 }+ 2b^{2} – 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 y ^{2} = 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 x ^{2} = 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 y ^{2} = – 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 x ^{2} = – 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 y ^{2} = 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 x ^{2} = – 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 49x ^{2} + 9y^{2 }= 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 4x ^{2} + 16y^{2 }= 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 4x ^{2} + y^{2 }= 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 y ^{2} – 4 x^{2} = 100**

**Q.4: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 9 x ^{2} – 4 y^{2} = 36**

**Q.5: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 6 y ^{2} – 16 x^{2} = 96**

**Q.6: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 64 y ^{2} – 9 x^{2} = 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)**