K-deformed conic sections

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Juan Carlos Arango Parra http://orcid.org/0000-0002-8862-7478 Héctor Román Quiceno Echavarría http://orcid.org/0000-0003-4399-823X Osiris Plata Lobo http://orcid.org/0000-0003-4882-8088

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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How to Cite
ARANGO PARRA, Juan Carlos; QUICENO ECHAVARRÍA, Héctor Román; PLATA LOBO, Osiris. K-deformed conic sections. Ingeniería y Ciencia | ing.cienc., [S.l.], v. 12, n. 24, p. 9-29, nov. 2016. ISSN 2256-4314. Available at: <http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/3536>. Date accessed: 22 sep. 2017. 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
Section
Articles

References

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