@noswald An #AlgebraicCurve is named by the order of the implicit polynomial equations describing them.

\[ \frac{1}{x^2} + \frac{1}{y^2} = 1 \Rightarrow x^2 y^2 - x^2 - y^2 = 0 \]

So it is a #quartic curve of the form 𝑥²𝑦²−𝑏²𝑥²−𝑎²𝑦²=0 which is called a #cruciform curve, cross curve, or sometimes the policeman on point duty curve.

https://mathworld.wolfram.com/Cruciform.html

https://en.wikipedia.org/wiki/Quartic_plane_curve#Cruciform_curve

https://www.statisticshowto.com/cruciform-curve/

https://en.wikipedia.org/wiki/Superellipse