Symmetry in elliptical coordinate

Question

Consider a function $f(x,y)$ in 2D. If it has symmetry in a circle I can write it as $f(r)$, which $r$ is radius in polar coordinate. How can I write it in elliptical coordinate if it has a elliptical symmetry? Can it be written as $f(v)$ or $f(\mu)$ if $v$ and $\mu$ are elliptical coordinate?