Circular Cubics and Quartics in Pseudo-Euclidean Plane Obtained by Inversion

The presentation is an extension of [N. Kovačević, V. Szirovicza, Inversion in Minkowskischer Geometrie. Math. Pann. 21/1 (2010), 89-113.] where the inversions in a pseudo-Euclidean plane with an equiform conic as the fundamental conic and a pole at its center or at an isotropic point have been studied. The type of circularity for the curves has also been introduced. We show that by using these transformations the cubics of all types of circularity can be constructed as images of conics. Unfortunately, the same does not hold for the quartics.