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The feet of the perpendicular from the origin on a variable chord of the circle \( x^{2}+y^{2}-2 x-2 y=0 \) is \( \mathrm{N} \). If the variable chord makes an angle of \( 90^{\circ} \) at the origin, then the locus of \( \mathrm{N} \) has the equation
\( \mathrm{P} \)
(A) \( x^{2}+y^{2}-x-y=0 \)
(B) \( x^{2}+y^{2}+x+y=0 \)
(C) \( x^{2}+y^{2}-2 x-2 y=0 \)
(D) \( x^{2}+y^{2}+2 x-2 y=0 \)
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