# Will polar curves always intersect?

The curves ${x}^{2} + {y}^{2} = 1$ and ${x}^{2} + {y}^{2} = 9$ are concentric circles with unequal radii. They do not intersect.
In polar form, these are the curves $r = 1$ and $r = 3$. (And, of course, they still do not intersect.)