The area of the ellipse $ \large\frac{x^2}{a^2} +\frac{y^2}{b^2} $$=1$ is $\pi a b$
The equation of the auxiliary circle of the ellipse $ \large\frac{x^2}{a^2} +\frac{y^2}{b^2} $ is $x^2+y^2$
Area of the auxiliary circle is
$x^2 +y^2 =a^2 \pi a^2$
Area between the auxiliary circle ad the ellipse $ = \pi a^2 - \pi ab$
$\qquad= \pi a (a-b)$
Hence 3 is the correct answer.