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=

# A vertical line passing through the point (h,0) intersects the ellipse $\frac{{\mathrm{x}}^{2}}{4}+\frac{{\mathrm{y}}^{2}}{3}=1$at the points P and Q. If the tangents to the ellipse at P and Q meet at the point R.If

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### Solution:

When $\mathrm{cos}\mathrm{\theta }=\frac{1}{4}=\frac{45\sqrt{5}}{8}{\mathrm{\Delta }}_{2}={\mathrm{\Delta }}_{min}$ occurs at
When

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