Shown here are images of the "equipotential" lines for various "charge" configurations of the [b][url=https://en.wikipedia.org/wiki/N-ellipse]n-ellipse/hyperbola[/url][/b], obtained using the [url=https://www.geogebra.org/m/vs9vqafh]applet[/url].
Inspired by the [url=https://www.math.ucdavis.edu/~deloera/MISC/LA-BIBLIO/trunk/nellipse.pdf]article[/url]