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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-10-CIR-01
Circle — Assignment
Chapter: Conic Sections
Topic: Circle
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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 centre of $(x-1)^2+(y-2)^2=9$ is:
  • A.$(1,2)$
  • B.$(-1,-2)$
  • C.$(2,1)$
  • D.$(1,-2)$
3.
The radius of $x^2+y^2=49$ is:
  • A.$49$
  • B.$7$
  • C.$\sqrt7$
  • D.$14$
4.
The centre of $x^2+y^2+2gx+2fy+c=0$ is:
  • A.$(g,f)$
  • B.$(-g,-f)$
  • C.$(c,c)$
  • D.$(0,0)$
5.
The radius of $x^2+y^2-4x=0$ is:
  • A.$1$
  • B.$2$
  • C.$4$
  • D.$\sqrt2$
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 centre and radius of $(x-3)^2+(y+1)^2=16$.
8.
Find the equation of the circle with centre $(1,2)$ and radius $3$.
9.
Find the radius of $x^2+y^2-6x-8y=0$.
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.
Find the equation of the circle with centre $(2,-3)$ passing through the origin.
12.
Find the equation of the circle with the segment joining $(1,2)$ and $(3,4)$ as diameter.
13.
Does the point $(3,4)$ lie on $x^2+y^2=25$?
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 centre and radius of $2x^2+2y^2-8x+12y-1=0$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $x^2+y^2=9$
  2. (A) $(1,2)$
  3. (B) $7$
  4. (B) $(-g,-f)$
  5. (B) $2$
Section B — Short Answer (2 marks)
  1. $x^2+y^2=25$.
  2. Centre $(3,-1)$, radius $4$.
  3. $(x-1)^2+(y-2)^2=9$.
  4. $5$ (centre $(3,4)$).
Section C — Short Answer (3 marks)
  1. Centre $(2,3)$, radius $5$.
  2. $(x-2)^2+(y+3)^2=13$.
  3. $(x-2)^2+(y-3)^2=2$.
  4. Yes, it lies on the circle.
Section D — Long Answer (5 marks)
  1. $x^2+y^2-4x-6y=0$.
  2. Centre $(2,-3)$, radius $\dfrac{3\sqrt6}{2}$.
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