Tangents are drawn to the hyperbola \( 4 x^{2}-y^{2}=36 \) at the point \( \mathrm{P} \) and \( ...

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Tangents are drawn to the hyperbola \( 4 x^{2}-y^{2}=36 \) at the point \( \mathrm{P} \) and \( \mathrm{Q} \). If these tangents intersect at the point \( \mathrm{T}(0,3) \) then the area (in sq. units) of \( \triangle \mathrm{PTQ} \) is -
[JEE Main - 2018]
(1) \( 54 \sqrt{3} \)
(2) \( 60 \sqrt{3} \)
(3) \( 36 \sqrt{5} \)
(4) \( 45 \sqrt{5} \)
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