Comprehension The vertices of a \( \triangle A B C \) lies on a rectangular hyperbola such that ...

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Comprehension
The vertices of a \( \triangle A B C \) lies on a rectangular hyperbola such that the orthocentre of the triangle is \( (3,2) \) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axis. If the two perpendicular tangents of the hyperbola intersect at the point \( (1,1) \).
Equation of the rectangular hyperbola is
(a) \( x y=2 x+y-2 \)
(b) \( 2 x y=x+2 y+5 \)
(c) \( x y=x+y+1 \)
(d) None of these
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