Resumo

ARANGO-PARRA, Juan Carlos; QUICENO-ECHAVARRIA, Hector Roman  e  PLATA-LOBO, Osiris. κ-Deformed Conic Sections. ing.cienc. [online]. 2016, vol.12, n.24, pp.9-29. ISSN 1794-9165.  https://doi.org/10.17230/ingciencia.12.24.1.

In this paper we study the effects of the κ-deformed sum, defined as, on the Euclidean distance function d(P, F 1) + d(P, F 2) = 2a, where P is an arbitrary point in R 2 ; F 1 and F 2 are the focus of the curve named Ellipse. The points satisfying the resulting equality d(P, F 1) d(P, F2) = 2a, describe a curve named κ-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 κ-deformed conic sections: Ellipse, hyperbola, circumference and parábola in the κ-deformed setting. We also make a study of the area of the regions limited by the κ-deformed ellipse and hyperbola for an arbitrary value of κ.

Palavras-chave : κ-deformed sum and difference; κ-deformed ellipse; κ-deformed circle; κ-deformed parabola; κ-deformed hyperbola.

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