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Q.
Tangents are drawn to the hyperbola $4x^2 - y^2 = 36$ at the points $P$ and $Q$. If these tangents intersect at
the point $T(0, 3)$ then the area (in sq. units) of $\Delta PTQ$ is :
Clearly $P Q$ is a chord of contact,
i.e., equation of $P Q$ is $T \equiv 0$
$\Rightarrow y=-12$
Solving with the curve, $4 x^{2}-y^{2}=36$
$\Rightarrow x=\pm 3 \sqrt{5}, y=-12$
i.e., $P(3 \sqrt{5},-12) ; Q(-3 \sqrt{5},-12) ; T(0,3)$
Area of $\Delta P Q T$ is
$\Delta=\frac{1}{2} \times 6 \sqrt{5} \times 15$
$=45 \sqrt{5}$