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UPSC NDA I 2014 Mathematics Paper

DIRECTIONS: (For the next two (02) items that follow):

Consider an ellipse

\;\frac{x^{2}}{a^{2}}+\;\frac{y^{2}}{b^{2}}=1

[NDA I 2014]

Question : 85 of 120

Marks: +1, -0

Solution:

Let ∠AOM = θ, then point A be (acosθ,sinθ)

The length of rectangle = 2acosθ

The width of rectangle = 2bsinθ

Area = 4absinθcosθ = 2absin2θ

For maximum sin2θ = 1

Area_{\max}=2ab

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