Answer
Center (in polar coordinates): $(2,0)$
Radius $=2$
Work Step by Step
A circle passing through the origin, of radius $a$, centered at $P_{0}(r_{0}, \theta_{0}),$ has the polar equation
$r=2a\cos(\theta-\theta_{0})$
For $\theta=\pi/2,\ r=0$, so $(0,0) $ is on the circle.
$2a=4$, so the radius is $r_{0}=2$.
Also, the angle $(\theta-\theta_{0})=\theta=(\theta-0)$,
so $\theta_{0}=0$ (the center lies on the +x axis).
Center (in polar coordinates):$\quad (2,0)$
Radius $=2$
