Question

The area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is (in sq. units)

• A. $12$
• B. $48$
• C. $7$
• D. $24$

Answer 1

The correct option is D $24$


The area of the rectangle is,
$A=6\sin \theta \times 8\cos \theta \Rightarrow A=48\sin \theta \cos \theta \Rightarrow A=24\sin 2\theta$
The maximum possible area is,
$A_{max.}=24$