Secciones cónicas κ-deformadas.

In this paper we study the effects of the κ-deformed sum, defined as x...y = x√1 + κ²y² + y√1 + κ²x², 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 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. [ABSTRACT FROM AUTHOR]