\( \mathrm{P} \) The vertices of \( \triangle A B C \) lie on a rec...

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\( \mathrm{P} \)
The vertices of \( \triangle A B C \) lie on a rectangular hyperbola such
W that the orthocentre of the triangle is \( (2,3) \) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point \( (1,1) \).
The equation of the rectangular hyperbola is
(1) \( x y-5=y-x \)
(2) \( x y+1=x+y \)
(3) \( x y=x+y+1 \)
(4) \( x y-11=-x-y \)
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