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...

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Autores:
Arango Parra, Juan Carlos
Quiceno Echavarría, Héctor Román
Plata Lobo, Osiris
Tipo de recurso:
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
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Copyright (c) 2016 Ingeniería y Ciencia | ing.cienc.
Description
Summary: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.