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The equation of a circle which passes through $(2 a, 0)$ and whose radical axis in relation to the circle $x^{2} + y^{2} = a^{2}$ is $x = a / 2,$ is

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x2+y2−ax=0

x2+y2+2ax=0

x2+y2−2ax=0

x2+y2+ax=0

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detailed solution

Correct option is C

The required circle isx2+y2−a2+λx−a2=0 [Using: S+λL=0 ] This passes through (2a,0)∴ 4a2−a2+3a2λ=0⇒λ=−2aHence, the required circle is x2+y2−a2−2ax−a2=0⇒x2+y2−a2−2ax+a2=0⇒x2+y2−2ax=0

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The equation of a circle which passes through (2a, 0) and whose radical axis in relation to the circle x2+y2=a2 is x=a/2, is

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Ready to Test Your Skills?

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The equation of a circle which passes through $(2 a, 0)$ and whose radical axis in relation to the circle $x^{2} + y^{2} = a^{2}$ is $x = a / 2,$ is