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

• Correct answer
  A

  $2 a b$
• B

  $a b$
• C

  $3a b$
• D

  $\frac{a}{b}$

Solution

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 $\sin 2 \theta=1$.

Hence, the correct answer is option: 'A'.