JEE Main On 08 April 2018 Question 4
Question: 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: [JEE Main Online 08-04-2018]
Options:
A) $ 60\sqrt{3} $
B) $ 36\sqrt{5} $
C) $ 45\sqrt{5} $
D) $ 54\sqrt{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \frac{x^{2}}{9}-\frac{y^{2}}{36}=1 $
Equation of $ P{Q _{(T=0)}}\to 0-\frac{y}{12}=1 $
$ \because \text{P }\And\text{ Q are (}\pm 3\sqrt{5},-12) $
$ \therefore \text{ Area =}\frac{1}{2}6\sqrt{5}\times 15=45\sqrt{5} $
