Locus of intersection of two perpendicular tangents to the hyperbola is:
Step-by-Step Solution
Key Concept: The director circle of a hyperbola uses $b^2 = a^2(e^2-1)$ and can yield no real points when $a^2 < b^2$.
The director circle of a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is found using the centre (midpoint of foci) at $(h,k) = (3, \frac{7}{2})$ and the relation $b^2 = a^2(e^2-1)$. With $a = \frac{3}{2}$, $e = \frac{5}{3}$, we get $b^2 = 4$. The director circle equation becomes $(x-3)^2 + (y-\frac{7}{2})^2 = \frac{7}{4}$, which does not represent any real point.
Correct Answer: 4