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 $=\pi a^2-\pi ab=\pi a(a-b)$