Evolutes of conics in the quasi-hyperbolic and the hyperbolic plane.

The evolute of a conic is a curve of order six and class four in the general case. This paper is an extension of Božić Dragun (Mathematica Pannonica 29, 77–86, 2023) where we discuss and compute the order and class of evolutes of different types of conics in the pseudo-Euclidean plane. In this paper we will emphasize on the evolute’s characteristics related to Plücker formulas in the conveniently selected model of the quasi-hyperbolic plane and the projectively extended hyperbolic plane. Also construction details of the evolute of a conic in the projectively extended hyperbolic plane will be shown. [ABSTRACT FROM AUTHOR]