JEE Advanced 2013 Paper 1 Mathematics Q19

Mathematics

Problem

A vertical line passing through the point (h,0)(h,0) intersects the ellipse x2/4+y2/3=1x^2/4+y^2/3=1 at the points PP and QQ. Let the tangents to the ellipse at PP and QQ meet at the point RR. If Δ(h)\Delta(h) = area of the triangle PQRPQR, Δ1=max⁡1/2≤h≤1Δ(h)\Delta_1=\max_{1/2\le h\le1}\Delta(h) and Δ2=min⁡1/2≤h≤1Δ(h)\Delta_2=\min_{1/2\le h\le1}\Delta(h), then 85Δ1−8Δ2\dfrac{8}{\sqrt{5}}\Delta_1-8\Delta_2 =

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