EJMT Abstract

Hyperbolism of a given curve with respect to a point and a line is an interesting construct, a special kind of geometric locus, not frequent in the literature. While networking between two different kinds of mathematical software, we explore various cases, involving quartics, among them the so-called Külp quartic and topologically equivalent curves, and also an example with a sextic and a curve of degree 12. By a similar but different way, we derive a new construction of a lemniscate of Gerono. First, parametric equations are derived for the curve, then we perform implicitization Gr¨obner bases packages and using elimination. The polynomial equation which is obtained enables to check irreducibility of the constructed curve.