Question

The area of the region enclosed between the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and its auxiliary circle is

• A. $\pi (a - b)^2$
• B. $\pi (a + b)^2$
• C. $\pi a (a - b) $
• D. $\pi^2 (a + b)$

Answer 1

Answer: (C)

Equation of auxiliary circle
$\Rightarrow \:\: x^2 + y^2 = a^2 (a > b)$
$ \therefore $ Required area = Area of circle - Area of ellipse $ = \pi a^2 - \pi ab = \pi a (a -b)$