For which of the hyperbolas, can we have more than one pair of perpendicular tangents? `(x^2)/4-(y^2)/9=1` (b) `(x^2)/4-(y^2)/9=-1` `x^2-y^2=4` (d) `x y=44`

Options

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`

Answer

B

Explanation

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.