Circular curves of the 3rd class in the quasi- hyperbolic plane obtained by projective mapping

The metric in the quasi-hyperbolic is induced by an absolute figure F_QH = {;F, f_1, f_2};, consisting of two real lines f_1 and f_2 incidental with the real point F. A curve of class n is circular in the quasi-hyperbolic plane if it contains at least one absolute line. The curves of the 3rd class can be obtained by projective mapping i.e. obtained by projectively linked pencil of curves of the 2nd class and range of points. The circular curves of the 3rd class of all types, depending on their position to the absolute fi gure, can be constructed with projectively linked pencils.