Tangents are drawn to the hyperbola 4x2 - y2 = 36 at the point P and Q. If these tangents intersect

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Tangents are drawn to the hyperbola 4x2 - y2 = 36 at the point P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of &#8710;PTQ is -

Accepted Answer

Equation PQ : chord of contact T = 0
y = - 12

$\frac{x^{2}}{9} - \frac{y^{2}}{36} = 1$
Area : $\frac{1}{2} P Q . T R$
TR = 3 + 12 = 15, Point P $(3 \sqrt{5}, - 12)$
$\Rightarrow P Q = 6 \sqrt{5}$
Area of $∆ P T Q = \frac{1}{2} . 15.6 \sqrt{5} = 45 \sqrt{5}$ sq. units

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