Answer
The region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Work Step by Step
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 $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
