On Foci and Asymptotes of Conics in the Isotropic Plane

Source abstract

The paper shows that every conic with foci in the isotropic plane can be represented by the equation of the form $y^2=\epsilon x^2+x$, where $\epsilon \in \{-1, 0, 1\}$ for an ellipse, a parabola and a hyperbola with foci respectively. Using this equation some important properties of the foci are proved. According to duality the properties of asymptotes of the hyperbola in the isotropic plane are valid as well. 2000 Mathematics Subject Classification. 51N25