## Precalculus (6th Edition) Blitzer

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.