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Equidistant Sets of Conic and Line

  • Mirela Katić ŽlepaloEmail author
  • Ema Jurkin
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)

Abstract

In the paper we study equidistant sets (midsets) of a conic and a line. We show that it is a part of a curve of order 8 if the conic is an ellipse or a hyperbola, and it is a part of a curve of order 6 in the case of parabola. We study the properties of the obtained curves such as their behavior at infinity and the existence of singular points.

Keywords

Equidistant set (midset) Conic Singular point 

References

  1. 1.
    Ponce, M., Santibáñez, P.: On equidistant sets and generalized conics: the old and the new. Amer. Math. Monthly 121(1), 18–32 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Wilker, J.B.: Equidistant sets and their connectivity properties. Proc. Amer. Math. Soc. 47(2), 449–452 (1975)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringZagreb University of Applied SciencesZagrebCroatia
  2. 2.Faculty of Mining, Geology and Petroleum EngineeringUniversity of ZagrebZagrebCroatia

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