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Locus of the midpoint of chord of $x^{2} {+y}^{2} {=a}^{2}$ such that these chords cut the curve $x^{2} - 2 x - 2 y = 0$ at A and B , AB subtends right angle at the origin is _____

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$x^{2} {+y}^{2} -2x-2y=0$

$x^{2} {+y}^{2} -x-y=0$

$x^{2} {+y}^{2} -2x+2y=0$

$x^{2} + y^{2} - 2 x - y = 0$

answer is A.

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Detailed Solution

$s_{1} = s_{11} \Rightarrow h x + k y = h^{2} + k^{2}$

By Homogenising

$a+b=0$

$\Rightarrow a+b=0$

$\Rightarrow h^{2} + k^{2} - 2 h - 2 k = 0$

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