Question

The area of the rectangle of maximum area inscribed in the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is

• A. $48$
• B. $41$
• C. $40$
• D. $50$

Answer 1

The correct option is C $40$

Given equation of ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$

Area of rectangle inscribed in an ellipse $=\frac{1}{2}\left(2a\right)\left(2b\right)=2ab$
Here $a=5,b=4$
Area of rectangle $=\frac{1}{2}(2\times 5)(2\times 4)$

$=40$ sq.units