The area of circle circumscribing $x = \frac{-3h}{2}$ is:
Step-by-Step Solution
Key Concept: The circumcircle of a triangle formed by a point and two tangent points has its diameter determined by the angle subtended at the radical center.
The circumcircle of $\triangle TAB$ has $TC_3$ as diameter. With $TC_3 = \frac{TA}{\cos\left(\frac{\theta_1 + \theta_2}{2}\right)} = \frac{4}{\frac{1}{\sqrt{5}}} = 4\sqrt{5}$, the area is $\pi\left(2\sqrt{5}\right)^2 = 20\pi$.
Correct Answer: 2