Consider the ellipse x^2 9 + y^2 4 =1. Let S(p, q) be a point in the first quadrant such that p^2 9 + q^2 4 1. Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let R b

Question

Consider the ellipse x^2 9 + y^2 4 =1. Let S(p, q) be a point in the first quadrant such that p^2 9 + q^2 4 >1. Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let R be the vertex of the ellipse with positive x-coordinate and O be the center of the ellipse. If the area of the triangle O R T is 3 2 , then which of the following options is correct?

Quantrex Academy · Accepted Answer

Correct answer: A. q=2, p=3 3

Ar ( ORT )= 3 2 | 1 2 3 2 |= 3 2 = 1 2 = 11 6 as point T is in third quadrant T ( 3 3 2 ,-1 ) Tanget at (0,2) x(0) 9 + y(2) 4 =1 y=2...(1) Tangent at ( 3 3 2 ,-1 ) x ( 3 3 2 ) 9 + y(-1) 4 =1...(2) By solving (1) & (2) p =3 3 , q =2 Option (1) is Correct.

JEE Advanced Mathematics Question (2024) — Solution

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