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Question

Area of the greatest rectangle that can be inscribed in the ellipse x2a2+y2b2=1 is:

A
2ab
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B
ab
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C
ab
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D
ab
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Solution

The correct option is A 2ab
Area of rectangle ABCD=(2acosθ).(2bsinθ)=2absin2θ
Area of greatest rectangle is equal to 2ab, when sin2θ=1 (maximum)

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