A vertical line passing through the point intersects the ellipse at the points and

MATHEMATICS · Numerical · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A vertical line passing through the point (h,0)(h, 0) intersects the ellipse x24+y23=1\frac{x^2}{4} + \frac{y^2}{3} = 1 at the points PP and QQ. If the tangents to the ellipse at PP and QQ meet at the point RR, and Δ(h)\Delta(h) is the area of △PQR\triangle PQR, Δ1=max⁡1/2≤h≤1Δ(h)\Delta_1 = \max_{1/2 \le h \le 1} \Delta(h) and Δ2=min⁡1/2≤h≤1Δ(h)\Delta_2 = \min_{1/2 \le h \le 1} \Delta(h), then 85Δ1−8Δ2\frac{8}{\sqrt{5}}\Delta_1 - 8\Delta_2 is equal to

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