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# NCERT solutions Mathematics Class 11 chapter 11 Conic Sections

## Chapter 11 - Conic Sections

#### Page 241

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

Q 1 | Page 241

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

Q 2 | Page 241

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

Q 3 | Page 241

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

Q 4 | Page 241

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

Q 5 | Page 241

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

Q 6 | Page 241

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

Q 7 | Page 241

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

Q 8 | Page 241

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

Q 9 | 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.

Q 10 | 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.

Q 11 | Page 241

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

Q 12 | Page 241

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

Q 13 | Page 241

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

Q 14 | Page 241

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

Q 15 | Page 241

#### Pages 246 - 247

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

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 x2 = 6y

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 y2 = – 8x

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 x2 = – 16y

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 y2 = 10x

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 x2 = –9y

Q 6 | Page 246

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

Q 7 | Page 247

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

Q 8 | Page 247

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

Q 9 | Page 247

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

Q 10 | 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

Q 11 | 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

Q 12 | Page 247

#### 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

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^2/4 + y^2/25 = 1

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^2/16 + y^2/9 = 1

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^2/25 + y^2/100 = 1

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^2/49 + y^2/36 = 1

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^2/100 + y^2/400 = 1

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 36x2 + 4y2 = 144

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 16x2 + y2 = 16

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 4x2 + 9y2 = 36

Q 9 | Page 255

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

Q 10 | Page 255

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

Q 11 | Page 255

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

Q 12 | 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)

Q 13 | 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)

Q 14 | Page 255

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

Q 15 | Page 255

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

Q 16 | Page 255

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

Q 17 | 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.

Q 18 | 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)

Q 19 | 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).

Q 20 | Page 255

#### 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

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 y^2/9 - x^2/27 = 1

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 9y2 – 4x2 = 36

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 16x2 – 9y2 = 576

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 5y2 – 9x2 = 36

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 49y2 – 16x2 = 784

Q 6 | Page 262

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

Q 7 | Page 262

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

Q 8 | Page 262

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

Q 9 | Page 262

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

Q 10 | Page 262

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

Q 11 | Page 262

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

Q 12 | Page 262

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

Q 13 | Page 262

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

Q 14 | Page 262

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

Q 15 | Page 262

#### Page 264

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

Q 1 | 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?

Q 2 | 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.

Q 3 | 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.

Q 4 | 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.

Q 5 | 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.

Q 6 | 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.

Q 7 | 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.

Q 8 | Page 264

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