If the angle between the asymptotes of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is 120⁰ and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be

 The product of perpendiculars drawn from the foci upon any of its tangents is 9. Therefore,
$\begin{array}{l}{\mathrm{b}}^2=9\\ \mathrm{also}, \frac{\mathrm{b}}{\mathrm{a}}=\tan {30}^{\circ }=\frac{1}{\sqrt{3}}\end{array}$

$\therefore a^2=3b^2=27$

Therefore, the required locus is the director circle of the hyperbola which is given by 

$\begin{array}{r}{\mathrm{x}}^2+{\mathrm{y}}^2=27-9\\ {\mathrm{x}}^2+{\mathrm{y}}^2=18\end{array}$

$\mathrm{b}/\mathrm{a}=\tan {60}^{\circ }$

$a^2=\frac{b^2}{3}=\frac{9}{3}=3$

${\text{ Hence,therequiredlocusis x}}^2+y^2=3-9=-6 \text{whichisnot possible}.$