Answer
Center at$\displaystyle \quad (4,-\frac{\pi}{2})$
Radius $=4$
Work Step by Step
For $\theta=0,\ r=0$, so the origin is on the circle.
A circle passing through the origin, of radius $a$, centered at $P_{0}(r_{0}, \theta_{0}),$
has the polar equation
$r=2a\cos(\theta-\theta_{0})$
Applying the trigonometric identity
$ \displaystyle \cos(\theta\pm\frac{\pi}{2})=\mp\sin\theta$,
we rewrite the equation:
$r=2(4)\displaystyle \cos(\theta+\frac{\pi}{2}),\qquad a=4, \theta_{0}=-\frac{\pi}{2}$
Center at$\displaystyle \quad (4,-\frac{\pi}{2})$
Radius $=4$
