Question

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

Answer 1

Answer: (B)

Let $P Q R S$ be a rectangle, where $P$ is $(a \cos \theta, b \sin \theta)$
$\therefore \quad \text { Area of rectangle } =4(a \cos \theta),(b \sin \theta) $
$ =2 a b \sin 2 \theta$
This is maximum when $\sin 2 \theta=1$
Hence, maximum area $=2 ab (1)=2 ab $