1.

The vertices of DeltaABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) 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

Answer»

`xy=2x+y-2`
`2xy=x+2y+5`
`xy=x+y+1`
NONE of these

Solution :LET the equation of the HYPERBOLA be `xy-x-y+1+lambda=0`.
It PASSES through (3,2). Hence, `lambda=-2`.
So, the equation of hyperbola is
`xy=x+y+1`


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