Engineering
Mathematics
Introduction to Determinants
Question

Consider the ellipse x29+y24=1. Let S(p, q) be a point in the first quadrant such that p29+q24>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 ΔORT is 32, then which of the following options is correct ?

q=2,p=33

q=2,p=43

q=1,p=53

q=1,p=63

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Solution
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Ar(ΔORT)=32

12×3×2sinθ=32

sinθ=12θ=11π6

T332,1

Tanget at (0,2)x(0)9+y(2)4=1y=2                     ....(1)

Tangent at 332,1x3329+y(1)4=1         ....(2)

∴ By solving (1) & (2) p=33,q=2

⇒ option (A) is correct

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