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Question

The radius of the circle S is same as the radius of x2 + y2 2x + 4y 11 = 0 and the centre of S is the centre of x2 + y2 2x 4y + 11 = 0 . Find the equation of S.


A

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B

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C

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D

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Solution

The correct option is C


To find the equation of a circle, we need the centre and radius of the circle, In this problem, we are given two circles, using which we can find the centre and radius.
To find the radius
x2 + y2 2x + 4y 11 = 0 and S(our circle) has the same radius.
We know the radius of the circle x2 + y2 + 2gx + 2fy + c=0 is

g2 + f2 c

r = 12 + 22 + 11

=4

To find the centre:
We are given S and x2 + y2 2x 4y + 11 = 0 have the same centre
Centre of x2 + y2 + 2gx + 2fy + c=0 is (g,f).
centre of x2 + y2 2x 4y + 11 = 0 is (1,2)
We got the centre (1,2) and radius (4) of the circle.
Equation is (x1)2 + (y2)2 = 42

x2 + y2 2x 4y + 1 + 4 = 16

x2 + y2 2x 4y 11 = 0


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