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Question

The equation of the common chord of the circles (x−a)2+(y−b)2=c2 and (x−b)2+(y−a)2=c2 is


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 A


We know that the equation of common chord is S1−S2 = 0, Where S1 and S2 are the equations of given circles, therefore

(x−a)2+(y−b)2−c2−(x−b)2−(y−a)2+c2=0

⇒2bx−2ax+2ay−2by=0

⇒2(b−a)x−2(b−a)y=0⇒x−y=0


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