Answer
The region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Work Step by Step
Let us consider $u^2+v^2 \leq 1$
Also, we have $x=au\\ u=\dfrac{x}{a}$ (simplify)
and $y=bv \\ v=\dfrac{y}{b}$(simplify)
Therefore, the values of $u$ and $v$ are:
$u=\dfrac{x}{a}$ and $ v=\dfrac{y}{b}$
Thus, the equation of the ellipse is:
$(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Hence, the region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$