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A triangle has its vertices on a rectang...

A triangle has its vertices on a rectangular hyperbola. Prove that the orthocentre of the triangle also lies on the same hyperbola.

A

`xy-1=x-y`

B

`xy+1=x+y`

C

`2xy=x+y`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Perpendicular tangents intersect at the center of rectangular hyperbola. Hence, the center of the hyperbola is (1,1) and the equations of asymptotes are x - 1 = 0 and y - 1 = 0.
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CENGAGE PUBLICATION-HYPERBOLA-COMOREHENSION TYPE
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