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Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is
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2646 Upvotes
Verified Answer
The correct answer is:
$2 a b$
$2 a b$
Area of rectangle $A B C D=(2 a\cos \theta)$
$(2 b \sin \theta)=2 a b \sin 2 \theta$
$\Rightarrow$ Area of greatest rectangle is equal to
$2 a b$
when $\sin 2 \theta=1$.
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