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The number of points from where a pair of perpendiculartangents can be drawn to the hyperbola, `x^2 sec^2 alpha -y^2 cosec^2 alpha=1, alpha in (0, pi/4)`, is (A) 0 (B) 1 (C) 2 (D) infinite

A

0

B

1

C

2

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
D
`(x^(2))/(cos^(2)alpha) - (y^(2))/(sin^(2)alpha) =1`
Locus of perpendicular tangents is director circle,
`x^(2) + y^(2) = a^(2) - b^(2)`
or `x^(2)+y^(2) = cos^(2) alpha - sin^(2) alpha = cos 2 alpha`
But `0 lt alpha lt (pi)/(4)`
`0 lt 2 alpha lt (pi)/(2)`
So there are infinite points.
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