Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is

2 a b

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a b

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\sqrt{a b}

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\frac{a}{b}

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Solution

The correct option is A $2 a b$
Area of rectangle $A B C D = 2 a c o s θ (2 b s i n θ) = 2 a b s i n 2 θ$
$\Rightarrow$ Area of greatest rectangle is equal to $2 a b$
When $s i n 2 θ = 1$ .

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