On Foci and Asymptotes of Conics in the Isotropic Plane

Authors

  • J. Beban-Brkić Department of Geomatics, Faculty of Geodesy, University of Zagreb, Zagreb, Croatia
  • M. Šimić Faculty of Architecture, University of Zagreb, Zagreb, Croatia
  • V. Volenec Department of Mathematics, University of Zagreb, Zagreb, Croatia

DOI:

https://doi.org/10.5644/SJM.03.2.12

Keywords:

Isotropic plane, conic section, focus

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

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References

H. Sachs, Ebene isotrope Geometrie, Vieweg-Verlag, Braunschweig; Wiesbaden, 1987.

K. Strubecker, Geometrie in einer isotropen Ebene, Math. Naturw. Unterricht, 15 (1962-63), 297–306, 343–351, 385–394.

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Published

12.06.2024

How to Cite

Beban-Brkić, J. ., Šimić, M., & Volenec, V. (2024). On Foci and Asymptotes of Conics in the Isotropic Plane. Sarajevo Journal of Mathematics, 3(2), 257–266. https://doi.org/10.5644/SJM.03.2.12

Issue

Vol. 3 No. 2 (2007)

Section

Articles