The area between the ellipse $\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$=$1$ and its auxillary circle is

Question

$$\begin{array}{1 1}(1)\pi b(a-b)&(2)2\pi a(a-b)\\(3)\pi a(a-b)&(4)2\pi b(a-b)\end{array}$$