Let P be a variable point on the ellipse x2a2+y2b2=1 with foci S1 and S2. If A be the area of ΔPS1S2, then the maximum value of A, is
A
ab
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B
abe
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C
12ab
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D
12abe
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Solution
The correct option is Babe Let P(acosθ,bsinθ) be the variable point on the ellipse x2a2+y2b2=1. Then, A=Area(ΔPS1S2) ⇒A=12∣∣
∣∣acosθbsinθ1ae01−ae01∣∣
∣∣=12bsinθ×2ae=abesinθ Clearly, it is maximum when θ=π2 and the maximum value of A is abe.