Vidaara.orgClass 11 · Mathematics
CodeVID-M11-10-CT
Conic Sections — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The circle with centre origin and radius $3$ is:
- A.$x^2+y^2=3$
- B.$x^2+y^2=9$
- C.$x^2+y^2=6$
- D.$x+y=3$
2.
The focus of $y^2=4ax$ is:
- A.$(0,a)$
- B.$(a,0)$
- C.$(-a,0)$
- D.$(0,-a)$
3.
The standard ellipse is:
- A.$\tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1$
- B.$\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1$
- C.$x^2+y^2=r^2$
- D.$y^2=4ax$
4.
The centre of $(x-1)^2+(y-2)^2=9$ is:
- A.$(1,2)$
- B.$(-1,-2)$
- C.$(2,1)$
- D.$(1,-2)$
5.
The directrix of $y^2=4ax$ is:
- A.$x=a$
- B.$x=-a$
- C.$y=-a$
- D.$y=a$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Write the equation of the circle with centre origin and radius $5$.
7.
Find the focus of $y^2=12x$.
8.
Find $a$ and $b$ for $\tfrac{x^2}{25}+\tfrac{y^2}{9}=1$.
9.
Find the centre and radius of $(x-3)^2+(y+1)^2=16$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the centre and radius of $x^2+y^2-4x-6y-12=0$.
11.
For $y^2=20x$, find the focus, directrix and latus rectum.
12.
Find the foci and eccentricity of the ellipse $\tfrac{x^2}{16}+\tfrac{y^2}{9}=1$.
13.
Find the equation of the circle with centre $(2,-3)$ passing through the origin.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the equation of the circle passing through $(0,0),(4,0)$ and $(0,6)$.
15.
Find the equation of the parabola with vertex at the origin, axis along the y-axis, passing through $(4,2)$.
Answer Key
Section A — Multiple Choice Questions
- (B) $x^2+y^2=9$
- (B) $(a,0)$
- (A) $\tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1$
- (A) $(1,2)$
- (B) $x=-a$
Section B — Short Answer (2 marks)
- $x^2+y^2=25$.
- $(3,0)$.
- $a=5,\ b=3$.
- Centre $(3,-1)$, radius $4$.
Section C — Short Answer (3 marks)
- Centre $(2,3)$, radius $5$.
- Focus $(5,0)$, directrix $x=-5$, latus rectum $20$.
- Foci $(\pm\sqrt7,0)$, $e=\tfrac{\sqrt7}{4}$.
- $(x-2)^2+(y+3)^2=13$.
Section D — Long Answer (5 marks)
- $x^2+y^2-4x-6y=0$.
- $x^2=8y$.
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