Find the co-ordinates of the middle point of the chord which the ci...

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Find the co-ordinates of the middle point of the chord which the circle \( x^{2}+y^{2}-2 x+2 y-2=0 \) cuts off on the line \( y=x-1 \). Find also the equation of the locus of the middle point of all chords of the circle
\( \mathrm{P} \) which are parallel to the line \( y=x-1 \).

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