Hyperbola 2 Question 5

5. Tangents are drawn to the hyperbola 4x2y2=36 at the points P and Q. If these tangents intersect at the point T(0,3), then the area (in sq units) of PTQ is

(a) 455

(b) 543

(c) 603

(d) 365

(2018 Main)

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Answer:

Correct Answer: 5. (b)

Solution:

  1. Tangents are drawn to the hyperbola 4x2y2=36 at the point P and Q.

Tangent intersects at point T(0,3)

Clearly, PQ is chord of contact.

Equation of PQ is 3y=36

y=12

Solving the curve 4x2y2=36 and y=12,

we get x=±35

Area of PQT=12×PQ×ST=12(65×15)=455



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