K-deformed conic sections

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.

• Autores: Arango Parra, Juan Carlos; Quiceno Echavarría, Héctor Román; Plata Lobo, Osiris
• Fecha de publicación: 2016
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: spa
• OAI Identifier: oai:repository.eafit.edu.co:10784/11290
• Acceso en línea: http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/3536; http://hdl.handle.net/10784/11290
• Palabra clave: Mathematics; K-deformed sum and difference, K-deformed ellipse, K-deformed circle, K-deformed parabola, K-deformed hyperbola; MSC 00A05; Matemáticas; Suma y diferencia k-deformada; elipse k-deformada; circunferencia k-deformada; parábola k-deformada; hipérbola k-deformada; MSC 00A05
• License: Copyright (c) 2016 Ingeniería y Ciencia | ing.cienc.