Answer
$x^{2}+y^{2}\leq 4$
.
Work Step by Step
$\left\{\begin{array}{ll}
(x,y)=(r\cos\theta,r\sin\theta) & \\
r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x}
\end{array}\right.$
$r$ is the directed distance of the point from the pole.
$r=2$ defines all points at a distance of 2 units from the pole.
$0\leq r\leq 2$
describes all points on or inside the circle of radius 2.
In Cartesian coordinates,
$x^{2}+y^{2}\leq 4$
