Chapter 1.2, Problem 86AYU

Challenge Problem Limacon For a nonzero constant $a$ and $b$, find the intercepts of the graph of

${\left(x^2+y^2-ax\right)}^2=b^2\left(x^2+y^2\right)$

Then test for symmetry with respect to the $x$-axis, the $y$-axis, and the origin.