Some Properties of Special Hyperbolas in the Isotropic Plane

Abstract

In this paper we consider special hyperbolas circumscribed to the symmetral triangle of a given triangle. Considering some special cases of these hyperbolas we get equations of some special conics related to the triangles associated to a given triangle as e.g., the Jeˇrabek hyperbola of the tangential triangle of the given triangle and the circumscribed circle of the symmetral triangle which is also the polar circle of the given triangle. We investigate some other interesting properties of special hyperbolas circumscribed to the symmetral triangle of a given triangle.