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