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For which of the hyperbolas, can we have...

For which of the hyperbolas, can we have more than one pair of perpendicular tangents?

A

`(x^(2))/(4)-(y^(2))/(9)=1`

B

`(x^(2))/(4)-(y^(2))/(9)=-1`

C

`x^(2)-y^(2)=4`

D

`xy=44`

Text Solution

Verified by Experts

The correct Answer is:
B
The locus of the point of intersection of perpendicular tangents is director circle for
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
The equation of director circle is `x^(2)+y^(2)=a^(2)-b^(2)`which is real if a gt b.
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