If angle between asymptotes of hyperbola x^2/a^2 - y^2/b^2 = 1 is 120° and product of perpendiculars

Question

If angle between asymptotes of hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) is 120° and product of perpendiculars drown from foci upon its any tangent is 9, then locus of point of intersection of perpendicular tangents of the hyperbola can be

(a) x² + y² = 18

(b) x² + y² = 6

(c) x² + y² = 9

(d) x² + y² = 3

Answer 1

Correct option is (a) x² + y² = 18

Then equation of director circle is x² + y² = 3 – 9 = – 6 which is not possible.