Circular cubics and quartics obtained as pedal curves of conics in pseudo-Euclidean plane

We are analyzing pedal curves of conics in pseudo-euclidean plane. The aim of this paper is to determine the conditions that the generating conic has to fulfill in order to obtain a circular cubic or quartic of a certain type. We intend to show that whenever a quartic is obtained as a pedal curve of a conic, it can only be with the type of circularity (2, 2) while a cubic can be either with the type (2, 1) or (1, 1). The emphasis will be put on the curves with no analogue in the Euclidean plane.