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The quasi-hyperbolic plane is one of nine projective-metric planes where the absolute figure is the ordered triple j1 ; j2 ; F. It is dual to the pseudo-Euclidean plane. It is known for the fact that a pencil of parabolas, in the Euclidean and pseudo-Euclidean plane, can be set according to lines a ; b ; c. The focus points of all parabolas in the pencil lie on the circle circumscribed to the triangle given by lines a ; b ; c. The connection between the pencil of parabolas, Wallace-Simson lines and Steiner deltoid curve are studied and proved in [2]. Analogues theorems are valid in the pseudo- Euclidean plane. In this paper the dual theorems will be proved in quasi-hyperbolic plane.
Quasi-hyperbolic plane; pencil of parabolas; Wallace-Simson line; point A
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