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The number of points on the hyperbola (x...

The number of points on the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` from which mutually perpendicular tangents can be drawn to the circle `x^2+y^2=a^2` is/are (a) 0 (b) 2 (c) 3 (d) 4

A

0

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Director circle of the circle `x^(2)+y^(2)=a^(2)" is "x^(2)+y^(2)=2a^(2)`.
The semi-transverse axis is `sqrt3a`.
The radius of the circle is `sqrt2a`.
Hence, director circle and hyperbola do not intersect.
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