K-deformed conic sections

Juan Carlos Arango Parra, Héctor Román Quiceno Echavarría, Osiris Plata Lobo

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.


Keywords


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

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DOI: http://dx.doi.org/10.17230/ingciencia.12.24.1

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Ingeniería y Ciencia 
ISSN: 1794-9165 
EISSN: 2256-4314