This set of Class 11 Maths Chapter 11 Multiple Choice Questions & Answers (MCQs) focuses on “Conic Sections”. These MCQs are created based on the latest CBSE syllabus and the NCERT curriculum, offering valuable assistance for exam preparation.

1. Find the equation of circle with center at origin and radius 5 units.

a) x^{2}+y^{2}=25

b) x^{2}+y^{2}=5

c) x^{2}=25

d) y^{2}=25

View Answer

Explanation: Equation of circle with center at (a, b) and radius r units is

(x-a)

^{2}+(y-b)

^{2}=r

^{2}

So, equation of circle is (x-0)

^{2}+(y-0)

^{2}=5

^{2}=> x

^{2}+y

^{2}=25.

2. Find the equation of circle with center at (2, 5) and radius 5 units.

a) x^{2}+y^{2}+4x-10y+4=0

b) x^{2}+y^{2}-4x-10y+4=0

c) x^{2}+y^{2}+4x+10y+4=0

d) x^{2}+y^{2}+4x-10y-4=0

View Answer

Explanation: Equation of circle with center at (a, b) and radius r units is

(x-a)

^{2}+(y-b)

^{2}=r

^{2}

So, equation of circle is (x-2)

^{2}+(y-5)

^{2}=5

^{2}=> x

^{2}+y

^{2}-4x-10y+4=0.

3. Find the center of the circle with equation x^{2}+y^{2}-4x-10y+4=0.

a) (-2, 5)

b) (-2, -5)

c) (2, -5)

d) (2, 5)

View Answer

Explanation: Comparing the equation with general form x

^{2}+y

^{2}+2gx+2fy+c=0, we get

2g=-4 => g=-2

2f=-10 => f=-5

c=4

Center is at (-g, -f) i.e. (2, 5).

4. Find the radius of the circle with equation x^{2}+y^{2}-4x-10y+4=0.

a) 25 units

b) 20 units

c) 5 units

d) 10 units

View Answer

Explanation: Comparing the equation with general form x

^{2}+y

^{2}+2gx+2fy+c=0, we get

2g=-4 => g=-2

2f=-10 => f=-5

c=4

Radius = \(\sqrt{g^2+f^2-c} = \sqrt{4+25-4}\)=5.

5. Find the equation of circle which pass through (5, 9) and center at (2, 5).

a) x^{2}+y^{2}+4x-10y+4=0

b) x^{2}+y^{2}-4x-10y+4=0

c) x^{2}+y^{2}+4x+10y+4=0

d) x^{2}+y^{2}+4x-10y-4=0

View Answer

Explanation: Equation of circle with center at (a, b) and radius r units is

(x-a)

^{2}+ (y-b)

^{2}= r

^{2}

(5-2)

^{2}+ (9-5)

^{2}= r

^{2}=> r

^{2}=3

^{2}+4

^{2}=> r=5.

So, equation of circle is (x-2)

^{2}+(y-5)

^{2}=5

^{2}=> x

^{2}+y

^{2}-4x-10y+4=0.

6. If a circle pass through (2, 0) and (0, 4) and center at x-axis then find the radius of the circle.

a) 25 units

b) 20 units

c) 5 units

d) 10 units

View Answer

Explanation: Equation of circle with center at x-axis (a, 0) and radius r units is

(x-a)

^{2}+(y)

^{2}=r

^{2}

=>(2-a)

^{2}+(0)

^{2}=r

^{2}

And (0-a)

^{2}+(4)

^{2}=r

^{2}

=>(a-2)

^{2}=a

^{2}+4

^{2}=> (-2)(2a-2) =16 => a-1=-4 => a=-3

So, r

^{2}= (2+3)

^{2}=5

^{2}

r=5 units.

7. If a circle pass through (4, 0) and (0, 2) and center at y-axis then find the radius of the circle.

a) 25 units

b) 20 units

c) 5 units

d) 10 units

View Answer

Explanation: Equation of circle with center at y-axis (0, b) and radius r units is

(x)

^{2}+(y-b)

^{2}=r

^{2}

=>(4)

^{2}+(-b)

^{2}=r

^{2}

And (0)

^{2}+(2-b)

^{2}=r

^{2}

=>(b-2)

^{2}=b

^{2}+4

^{2}=> (-2)(2b-2)=16 => b-1=-4 => b=-3

So, r

^{2}=4

^{2}+3

^{2}=5

^{2}=> r=5 units.

8. The point (1, 4) lie ___________ the circle x^{2}+y^{2}-2x-4y+2=0.

a) inside circle

b) outside circle

c) on the circle

d) either inside or outside

View Answer

Explanation: Circle has equation x

^{2}+y

^{2}-2x-4y+2=0.

1

^{2}+4

^{2}-2*1-4*4+2 = 1+16-2-16+2 =1 > 0 so, point is outside the circle.

9. The point (0, 0) lie ___________ the circle x^{2}+y^{2}-2x-4y=0.

a) inside circle

b) outside circle

c) on the circle

d) either inside or outside

View Answer

Explanation: Circle has equation x

^{2}+y

^{2}-2x-4y=0.

0

^{2}+0

^{2}-2*0-4*0+0 = 0 so, point is on the circle.

10. The point (6, 2) lie ___________ the circle x^{2}+y^{2}-2x-4y-36=0.

a) inside circle

b) outside circle

c) on the circle

d) either inside or outside

View Answer

Explanation: Circle has equation x

^{2}+y

^{2}-2x-4y-36=0.

6

^{2}+2

^{2}-2*6-4*2-36 = 36+4-12-8-36 =-16<0 so, point is inside the circle.

**More MCQs on Class 11 Maths Chapter 11:**

- Chapter 11 – Conic Sections MCQ (Set 2)
- Chapter 11 – Conic Sections MCQ (Set 3)
- Chapter 11 – Conic Sections MCQ (Set 4)
- Chapter 11 – Conic Sections MCQ (Set 5)

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