Answer
To test for symmetry with respect to the pole (origin), replace r with –r; if an equivalent equation results, the graph is symmetric with respect to the pole.
Work Step by Step
For example:
We will replace $r\,\text{with}\,-r$ in the polar equation $r=1-2\cos \theta $, to perform the test for the pole,
$\begin{align}
& r=1-2\cos \theta \\
& -r=1-2\cos \theta
\end{align}$
The resultant equation changes and thus it fails this symmetry test.
