\( \mathrm{A}(1,0) \) and \( \mathrm{B}(0,1) \) are two fixed point...

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\( \mathrm{A}(1,0) \) and \( \mathrm{B}(0,1) \) are two fixed points on the circle \( \mathrm{x}^{2}+\mathrm{y}^{2}=1 \). C is a variable point on this circle. As \( \mathrm{C} \) moves, the locus of the orthocentre of the triangle \( \mathrm{ABC} \) is
\( \mathrm{P} \)
(A) \( x^{2}+y^{2}-2 x-2 y+1=0 \)
(B) \( x^{2}+y^{2}-x-y=0 \)
(C) \( x^{2}+y^{2}=4 \)
(D) \( x^{2}+y^{2}+2 x-2 y+1=0 \)
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