JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Tangents are drawn to the hyperbola \(4{x^2} - {y^2} = 36\) 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 :
- A \(54\sqrt 3 \)
- B \(60\sqrt 3 \)
- C \(36\sqrt 5 \)
- D \(45\)\(\sqrt 5 \)
Answer & Solution
Correct Answer
(D) \(45\)\(\sqrt 5 \)
Step-by-step Solution
Detailed explanation
(4) Here equation of hyperbola is \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{{36}} = 1\) Now, \(PQ\) is the chord of contant \(\therefore \) Equation of \(PQ\) is \(\,:\frac{{x\left( 0 \right)}}{9} - \frac{{y\left( 3 \right)}}{{36}} = 1\) \( \Rightarrow y = - 12\) \(\therefore \) Area…
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