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On some properties of Kiepert parabola in the isotropic plane

In this paper we consider the curve which is an envelope of the axes of homology of a given triangle and the corresponding Kiepert triangles in the isotropic plane - the Kiepert parabola of the given triangle. We derive the equation of this parabola by using appropriate coordinate system. We give some new significant characterizations of this curve which are not valid in the Euclidean plane. We have also studied the relationships between Kiepert parabola and the Steiner point, the tangential triangle as well as the Jeřabek hyperbola of the given triangle.

isotropic plane, Kiepert parabola, Steiner point

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