## Calculus 8th Edition

The region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Given: $u^2+v^2 \leq 1$ Then , we have $x=au$ or, $u=\dfrac{x}{a}$ and $y=bv$ or, $v=\dfrac{y}{b}$ Therefore,we get $u=\dfrac{x}{a}$ and $v=\dfrac{y}{b}$ Now, $u^2+v^2 \leq 1 \implies (\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$ Hence, the region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$