Answer
$ r=12\cos\theta$
.
Work Step by Step
The circle passes through the origin, as (0,0) satisfies the Cartesian equation.
The radius is $6$, and the center is at $(6,0)$.
In polar coordinates, the center lies at $r_{0}=6, \theta_{0}=0,\qquad P(6,0)$
A circle passing through the origin, of radius $a$, centered at $P_{0}(r_{0}, \theta_{0}),$
has the polar equation
$ \quad r=2a\cos(\theta-\theta_{0})$
So this circle has the equation
$r=2(6)\cos(\theta-0)$
or
$ r=12\cos\theta$
