Answer
a. Cartesian, $(x-2)^{2}+(y -3)^{2}=5^{2}$.
b. Polar, $r=4$.
Work Step by Step
$a.$
The Cartesian equation here is $(x-2)^{2}+(y -3)^{2}=5^{2}$.
When the center is not at the origin, the polar equation will be harder to derive, since both r and $\theta$ vary from point to point.
$b.$
When the center is at the origin, the polar equation is $r=4,$ which is as simple as it gets.
The Cartesian is not too difficult, $x^{2}+y^{2}=4^{2}$, but the polar form is far simpler.
