Q.

A vertical line passing through the point (h,0) intersects the ellipse x24+y23=1at the points P and Q. If the tangents to the ellipse at P and Q meet at the point R.
If Δ(h)= area of the ΔPQR,Δ1=max1/2h1Δ(h)  and Δ2=min1/2h1Δ(h) then 85Δ18Δ2=

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answer is 9.

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Detailed Solution

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Δ1=Δmax occurs at cosθ=14=23sin3θcosθ
When cosθ=14=4558Δ2=Δmin occurs at  cos θ=12=23sin3 θcos θ
When cosθ=12=92 85Δ1Δ2=4536=9

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A vertical line passing through the point (h,0) intersects the ellipse x24+y23=1at the points P and Q. If the tangents to the ellipse at P and Q meet at the point R.If Δ(h)= area of the ΔPQR,Δ1=max1/2≤h≤1Δ(h)  and Δ2=min1/2≤h≤1 Δ(h) then 85Δ1−8Δ2=