Question

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

• A. $2ab$
• B. $ab$
• C. $\sqrt{ab}$
• D. $\frac{a}{b}$

Answer 1

The correct option is A $2ab$

Area of rectangle $ABCD=\left(2a\cos \theta \right).\left(2b\sin \theta \right)=2ab\sin 2\theta$

$\Rightarrow$ Area of greatest rectangle is equal to $2ab$, when $\sin 2\theta =1$ (maximum)