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

Question

Aicharya · Accepted Answer

Area of rectangle $A B C D=(2 a\cos 	heta)$ $(2 b \sin 	heta)=2 a b \sin 2 	heta$ $\Rightarrow$ Area of greatest rectangle is equal to $2 a b$ when $\sin 2 	heta=1$.

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

Solution