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= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Solution:

$Δ_{1} = Δ_{max} occurs at \cos θ = \frac{1}{4} = (\frac{2 \sqrt{3} \sin^{3} θ}{\cos θ})$
When $\cos θ = \frac{1}{4} = \frac{45 \sqrt{5}}{8} Δ_{2} = Δ_{min}$ occurs at $\cos θ = \frac{1}{2} = (\frac{2 \sqrt{3} \sin^{3} θ}{\cos θ})$
When $\cos θ = \frac{1}{2} = \frac{9}{2} ∴ \frac{8}{\sqrt{5}} Δ_{1} - Δ_{2} = 45 - 36 = 9$

Solution:

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