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Question

The equation of circle with centre (-a,-b) and radius a2-b2is


A

x2+y2+2ax+2by+2b2=0

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B

x2+y22ax2by2b2=0

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C

x2+y22ax2by+2b2=0

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D

x2+y22ax+2by+2a2=0

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Solution

The correct option is A

x2+y2+2ax+2by+2b2=0


Explanation for the correct option:

Finding the equation of the circle:

We know that the equation of circle with centre (x1,y1)and radius r is

x-x12+y-y12=r21

According to the given data,

x1=-a,y1=-bandr=a2-b2

Now substituting the values in equation 1 we get,

x--a2+y--b2=a2-b22x2+a2+2ax+y2+b2+2by=a2-b2x2+y2+2ax+2yb+2b2=0

Hence, option (A) is the correct answer.


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