Example 2. Find the area of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$.
$+\left(\frac{y}{b}\right)^{2}<1$ represents $S$. If $S_{0}$ denotes $x^{2}+y^{2}$ and $S_{0}=\pi$, then $S=\pi a b$.

