Tangents are drawn to the hyperbola $4x^2-y^2=36$ at the points $PandQ$  If these tangents Intersect at the point $T(0,3)$ then the area (in sq.units) of $\Delta PTQ$ is 

Let PQ  is chord of contact w.r.t point $T(0,3),$ then
Eqation of PQ is $4(0\times x)-(y\times 3)=36$ or $y=-12(S_1=0)$ 
Solving line PQ with the hyperbola, we get
$4x^2-144=36\Rightarrow 4x^2=180\Rightarrow x^2=45\Rightarrow x=\pm 3\sqrt{5}$ 
$\therefore P(-3\sqrt{5},-12),Q(3\sqrt{5},-12)$ 
  $\therefore$ Area of triangle $TPQ=\frac{1}{2}\times PQ\times TM=\frac{1}{2}\times \sqrt{5}\times 15=45\sqrt{5}sq.units$