# NCERT solutions for Class 11 Mathematics chapter 11 - Conic Sections [Latest edition]

## Solutions for Chapter 11: Conic Sections

Below listed, you can find solutions for Chapter 11 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.4Miscellaneous Exercise
Exercise 11.1 [Page 241]

### NCERT solutions for Class 11 Mathematics Chapter 11 Conic Sections Exercise 11.1 [Page 241]

Exercise 11.1 | Q 1 | Page 241

Find the equation of the circle with centre (0, 2) and radius 2

Exercise 11.1 | Q 2 | Page 241

Find the equation of the circle with centre (–2, 3) and radius 4

Exercise 11.1 | Q 3 | Page 241

Find the equation of the circle with (1/2, 1/4)and radius 1/12

Exercise 11.1 | Q 4 | Page 241

Find the equation of the circle with centre (1, 1) and radius sqrt2

Exercise 11.1 | Q 5 | Page 241

Find the equation of the circle with centre (–a, –b) and radius sqrt(a^2-b^2)

Exercise 11.1 | Q 6 | Page 241

Find the centre and radius of the circle (x + 5)2 + (y – 3)2 = 36

Exercise 11.1 | Q 7 | Page 241

Find the centre and radius of the circle x2 + y2 – 4x – 8y – 45 = 0

Exercise 11.1 | Q 8 | Page 241

Find the centre and radius of the circle x2 + y2 – 8x + 10y – 12 = 0

Exercise 11.1 | Q 9 | Page 241

Find the centre and radius of the circle 2x2 + 2y2 – x = 0

Exercise 11.1 | Q 10 | Page 241

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

Exercise 11.1 | Q 11 | Page 241

Find the equation of the circle passing through the points (2, 3) and (–1, 1) and whose centre is on the line – 3y – 11 = 0.

Exercise 11.1 | Q 12 | Page 241

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2, 3).

Exercise 11.1 | Q 13 | Page 241

Find the equation of the circle passing through (0, 0) and making intercepts and b on the coordinate axes.

Exercise 11.1 | Q 14 | Page 241

Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).

Exercise 11.1 | Q 15 | Page 241

Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?

Exercise 11.2 [Pages 246 - 247]

### NCERT solutions for Class 11 Mathematics Chapter 11 Conic Sections Exercise 11.2 [Pages 246 - 247]

Exercise 11.2 | Q 1 | Page 246

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = 12x

Exercise 11.2 | Q 2 | Page 246

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = 6y

Exercise 11.2 | Q 3 | Page 246

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = – 8x

Exercise 11.2 | Q 4 | Page 246

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = – 16y

Exercise 11.2 | Q 5 | Page 246

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = 10x

Exercise 11.2 | Q 6 | Page 246

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = –9y

Exercise 11.2 | Q 7 | Page 247

Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix x = –6

Exercise 11.2 | Q 8 | Page 247

Find the equation of the parabola that satisfies the following conditions: Focus (0, –3); directrix y = 3

Exercise 11.2 | Q 9 | Page 247

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

Exercise 11.2 | Q 10 | Page 247

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (–2, 0)

Exercise 11.2 | Q 11 | Page 247

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Exercise 11.2 | Q 12 | Page 247

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis

Exercise 11.3 [Page 255]

### NCERT solutions for Class 11 Mathematics Chapter 11 Conic Sections Exercise 11.3 [Page 255]

Exercise 11.3 | Q 1 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse  x^2/36 + y^2/16 = 1

Exercise 11.3 | Q 2 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse  x^2/4 + y^2/25 = 1

Exercise 11.3 | Q 3 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse x^2/16 + y^2/9 = 1

Exercise 11.3 | Q 4 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse x^2/25 + y^2/100 = 1

Exercise 11.3 | Q 5 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse  x^2/49 + y^2/36 = 1

Exercise 11.3 | Q 6 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse x^2/100 + y^2/400 = 1

Exercise 11.3 | Q 7 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36x2 + 4y2 = 144

Exercise 11.3 | Q 8 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 16x2 + y2 = 16

Exercise 11.3 | Q 9 | Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 4x2 + 9y2 = 36

Exercise 11.3 | Q 10 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

Exercise 11.3 | Q 11 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5)

Exercise 11.3 | Q 12 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0)

Exercise 11.3 | Q 13 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2)

Exercise 11.3 | Q 14 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (0, +- sqrt5), ends of minor axis (±1, 0)

Exercise 11.3 | Q 15 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)

Exercise 11.3 | Q 16 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

Exercise 11.3 | Q 17 | Page 255

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4

Exercise 11.3 | Q 18 | Page 255

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the axis.

Exercise 11.3 | Q 19 | Page 255

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)

Exercise 11.3 | Q 20 | Page 255

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).

Exercise 11.4 [Page 262]

### NCERT solutions for Class 11 Mathematics Chapter 11 Conic Sections Exercise 11.4 [Page 262]

Exercise 11.4 | Q 1 | Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola x^2/16 - y^2/9 = 1

Exercise 11.4 | Q 2 | Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola y^2/9 - x^2/27 = 1

Exercise 11.4 | Q 3 | Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9y2 – 4x2 = 36

Exercise 11.4 | Q 4 | Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 – 9y2 = 576

Exercise 11.4 | Q 5 | Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y2 – 9x2 = 36

Exercise 11.4 | Q 6 | Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y2 – 16x2 = 784

Exercise 11.4 | Q 7 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Exercise 11.4 | Q 8 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Exercise 11.4 | Q 9 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Exercise 11.4 | Q 10 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Exercise 11.4 | Q 11 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Exercise 11.4 | Q 12 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Foci (+-3sqrt5, 0), the latus rectum is of length 8

Exercise 11.4 | Q 13 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12

Exercise 11.4 | Q 14 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0), e = 4/3

Exercise 11.4 | Q 15 | Page 262

Find the equation of the hyperbola satisfying the give conditions: Foci (0, +- sqrt10), passing through (2, 3)

Miscellaneous Exercise [Page 264]

### NCERT solutions for Class 11 Mathematics Chapter 11 Conic Sections Miscellaneous Exercise [Page 264]

Miscellaneous Exercise | Q 1 | Page 264

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Miscellaneous Exercise | Q 2 | Page 264

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Miscellaneous Exercise | Q 3 | Page 264

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

Miscellaneous Exercise | Q 4 | Page 264

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Miscellaneous Exercise | Q 5 | Page 264

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Miscellaneous Exercise | Q 6 | Page 264

Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.

Miscellaneous Exercise | Q 7 | Page 264

A man running a racecourse notes that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.

Miscellaneous Exercise | Q 8 | Page 264

An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

## Solutions for Chapter 11: Conic Sections

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.4Miscellaneous Exercise

## NCERT solutions for Class 11 Mathematics chapter 11 - Conic Sections

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC 11 (Conic Sections) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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Concepts covered in Class 11 Mathematics chapter 11 Conic Sections are Sections of a Cone, Concept of Circle, Introduction of Parabola, Standard Equations of Parabola, Latus Rectum, Introduction of Ellipse, Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse, Special Cases of an Ellipse, Standard Equations of an Ellipse, Latus Rectum, Introduction of Hyperbola, Eccentricity, Standard Equation of Hyperbola, Latus Rectum, Standard Equation of a Circle, Eccentricity.

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