Answer
Center at$\quad (1,\pi)$
Radius $=1$
Work Step by Step
For $\displaystyle \theta=\frac{\pi}{2},\ r=0$, 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
$r=2a\cos(\theta-\theta_{0})$
Apply $\cos(\theta-\pi)=-\cos\theta$.
We can write this equation as
$ r=2(1)\cos(\theta-\pi),\qquad a=1, \theta_{0}=\pi$
Center at$\quad (1,\pi)$
Radius $=1$
