Question

$AOB$ is the positive quadrant of the ellipse $\frac{a^2}{b^2}+\frac{y^2}{b^2}1=1$ where $OA=a,OB=b$. Then area between the arc $AB$ and chord $AB$ of the ellipse is

• A. $\pi ab$
• B. $(\pi -2)ab)$
• C. $\frac{ab(\pi +2)}{2}$
• D. $\frac{ab}{4}(\pi -2)$

Answer 1

The correct option is D $\frac{ab}{4}(\pi -2)$

We know that Area of ellpise$=\pi ab$

$\Rightarrow$Therefore, Area of ellipse in $Q_1=\frac{\pi ab}{4}$

$\Rightarrow$Now, Area of triangle $=\frac{1}{2}ab$

$\Rightarrow$Hence required area$=\frac{1}{4}\pi ab-\frac{1}{2}ab=\frac{ab}{4}(\pi -2)$