Tangents are drawn to the hyperbola
Question:

Tangents are drawn to the hyperbola $4 x^{2}-y^{2}=36$ at the point $P$ and $Q$. If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\triangle P T Q$ is –

1. $54 \sqrt{3}$

2. $60 \sqrt{3}$

3. $36 \sqrt{5}$

4. $45 \sqrt{5}$

Correct Option: , 4

Solution: