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CBSE · Class 11 · Mathematics

Conic Sections

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The centre and radius of the circle x2 + y2 + 12x + 4y − 41 = 0 are:
  1. (−6, −2), 81
  2. (6, 2), 9
  3. (−12, −4), 9
  4. (−6, −2), 9
2.
The focus of the parabola x2 = 36y is:
  1. (0, 9)
  2. (9, 0)
  3. (0, −9)
  4. (0, 36)
3.
The eccentricity of the ellipse x2/25 + y2/169 = 1 is:
  1. 12/5
  2. 5/13
  3. 12/13
  4. 13/12
4.
The foci of the hyperbola x2/9 − y2/16 = 1 are:
  1. (±4, 0)
  2. (0, ±5)
  3. (±5, 0)
  4. (±3, 0)
5.
A circle is the set of points in a plane that are:
  1. at a fixed distance from a fixed point
  2. whose distances from two points add to a constant
  3. at a fixed distance from a fixed line
  4. equidistant from a point and a line
6.
The length of the latus rectum of x2/625 + y2/576 = 1 is:
  1. 48/25
  2. 625/12
  3. 576/25
  4. 1152/25
7.
The equation of the circle with centre (−6, 1) and radius 9 is:
  1. x2 + y2 + 12x − 2y − 44 = 0
  2. x2 + y2 + 6x − y − 44 = 0
  3. x2 + y2 − 12x + 2y − 44 = 0
  4. x2 + y2 + 12x − 2y + 118 = 0
8.
Assertion (A): For the ellipse x2/169 + y2/144 = 1, the foci are at (±5, 0).
Reason (R): For an ellipse, c2 = a2 + b2.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find the centre and radius of the circle x2 + y2 + 14x − 12y + 49 = 0.
10.
Find the equation of the circle with centre (−1, 1) that passes through (−5, 4).
11.
For the parabola y2 = −36x, find the focus, the axis, the equation of the directrix and the length of the latus rectum.
12.
Find the equation of the parabola with vertex at the origin, focus (0, 9) and directrix y = −9.
13.
For the ellipse x2/64 + y2/289 = 1, find the foci, the vertices, the lengths of the major and minor axes, the eccentricity and the length of the latus rectum.
14.
Find the equation of the ellipse with vertices (0, ±25) and foci (0, ±7).
15.
For the hyperbola x2/64 − y2/225 = 1, find the foci, the vertices, the eccentricity and the length of the latus rectum.
16.
Find the equation of the hyperbola with foci (±17, 0) and vertices (±15, 0).
Section C — Word problems4 × 4 = 16 marks
17.
Find the equation of the circle passing through (−13, −2), (−15, 4), (1, −4).
18.
Find the equation of the ellipse whose foci are (±4, 0) and whose major axis has length 10. Find also its eccentricity and latus rectum.
19.
Find the equation of the hyperbola with foci (0, ±17) and transverse axis of length 16. Find also its eccentricity.
20.
A parabola has its vertex at the origin, its axis along the x-axis, and passes through (2, 2). Find its equation, its focus and its directrix.
AmbifulWorksheets
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CBSE · Class 11 · Mathematics

Answer key

Conic Sections · AW-11M-CON-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) (−6, −2), 9complete the squares
2(a) (0, 9)4a = 36, so a = 9
3(c) 12/13c = √(169 − 25) = 12; e = c/a
4(c) (±5, 0)c2 = a2 + b2 = 25
5(a) at a fixed distance from a fixed point—
6(d) 1152/252b2/a = 2 × 576 ÷ 25
7(a) x2 + y2 + 12x − 2y − 44 = 0(x + 6)2 + (y − 1)2 = 81
8(c) A is true, but R is false.A is true: c = √(169 − 144) = 5. R is false.
9Centre (−7, 6), radius 6(x + 7)2 + (y − 6)2 = 36
10x2 + y2 + 2x − 2y − 23 = 0radius = √(42 + 32) = 5
11Focus (−9, 0); axis: the x-axis (y = 0); directrix x = 9; latus rectum 364a = −36
12x2 = 36ya = 9
13Foci (0, ±15); vertices (0, ±17); major axis 34, minor axis 16; e = 15/17; latus rectum 128/17c2 = a2 − b2 = 225
14x2/576 + y2/625 = 1b2 = a2 − c2 = 625 − 49 = 576
15Foci (±17, 0); vertices (±8, 0); e = 17/8; latus rectum 225/4c2 = a2 + b2 = 289
16x2/225 − y2/64 = 1b2 = c2 − a2 = 289 − 225 = 64
17x2 + y2 + 10x − 8y − 59 = 0 (centre (−5, 4), radius 10)substitute each point in x2 + y2 + Dx + Ey + F = 0 and solve for D, E, F
18x2/25 + y2/9 = 1; e = 4/5; latus rectum 18/5a = 5, c = 4, b2 = 9
19y2/64 − x2/225 = 1; e = 17/8a = 8, c = 17, b2 = c2 − a2 = 225
20y2 = 2x; focus (1/2, 0); directrix x = −1/2y2 = 4ax: 22 = 4a × 2