K-deformed conic sections

Authors

DOI:

https://doi.org/10.17230/ingciencia.12.24.1

Keywords:

K-deformed sum and difference, K-deformed ellipse, K-deformed circle, K-deformed parabola, K-deformed hyperbola

Abstract

In this paper we study the effects of the K-deformed sum, defined as   on the Euclidean distance function d(P, F1) + d(P, F2) = 2a, where P is an arbitrary point in R2 ; F1 and F2 are the focus of the curve named Ellipse. The points satisfying the resulting equality d(P, F1)  d(P, F2) = 2a, describe a curve named K-deformed ellipse for which the resulting analityc expression is analogue to the standard one. We make a deep study of the vertex, local extrema, asymptotes, the latus rectum and the graph of the resulting K-deformed conic ections: Ellipse, hyperbola, circumference and parábola in the K-deformed setting. We also make a study of the area of the regions limited by the -deformed ellipse and hyperbola for an arbitrary value of K.

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Author Biography

  • Juan Carlos Arango Parra, Docente de Cátedra Universidad Eafit, Universidad de Antioquia, nombramiento en propiedad Secretaría de Eduación
    Docente de cátedra Universidad Eafit, Universidad de Antioquia, nombrado en propiedad en la secretaría de Educación de Medellín.

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Published

2016-11-11

Issue

Vol. 12 No. 24 (2016)

Section

Articles

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How to Cite

Arango Parra, J. C., Quiceno Echavarría, H. R., & Plata Lobo, O. (2016). K-deformed conic sections. Ingeniería Y Ciencia, 12(24), 9-29. https://doi.org/10.17230/ingciencia.12.24.1