Answer
$r=2c\,cos\theta$
Work Step by Step
We are given that $x^{2}+y^{2}=2cx$.
We can use the cartesian-to-polar substitutions of $r^{2}=x^{2}+y^{2}$ and $x=rcos\theta$ to rewrite the expression as $r^{2}=2crcos\theta$.
Dividing both sides by $r$, we can rewrite the expression as $r=2c\,cos\theta$
