Answer
The region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Work Step by Step
In order to get the values of $u$ and $v$ we will need to solve the given two equations.
we have $u^2+v^2 \leq 1$
and $x=au\implies u=\dfrac{x}{a}$
Also, $y=bv \implies v=\dfrac{y}{b}$
Thus, we can write
$u=\dfrac{x}{a}$ and $ v=\dfrac{y}{b}$
This gives: $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Hence, the region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
