The locus of centre of a circle passing through (a, b) and cuts orthogonally to circle $x^{2} + y^{2} = p^{2}$ , is

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Solution

The correct option is A

Let equation of circle be $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ with $x^{2} + y^{2} = p^{2}$ cutting orthogonally, we get $0 + 0 = + c - p^{2}$

or $c = p^{2}$ and passing through (a, b), we get

$a^{2} + b^{2} + 2 g a + 2 f b + p^{2} = 0$ or

$2 a x + 2 b y - (a^{2} + b^{2} + p^{2}) = 0$

Required locus as centre (-g, -f) is changed to (x, y).

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