The equation of the locus of the middle point of a chord of the cir...

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The equation of the locus of the middle point of a chord of the circle \( x^{2}+y^{2}=2(x+y) \) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally
\( \mathrm{P} \) inclined to the \( x \)-axis is

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(a) \( x+y=2 \)
(b) \( x-y=2 \)
(c) \( 2 x-y=1 \)
(d) none of these
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