Elementary characterization with ellipses tangent to a line and a circle of the convex hull of a certain pair of circles. Caracterización elemental con elipses tangentes a una recta y un círculo de la envolvente convexa de un cierto par de círculos.

Abstract

In this work is given a characterization of the convex hull of the circles (x − 1)² + y² = 1/4 and (x + 1)² + y² = 1/4 through the union of the ellipses x² + 5y² − 4xy = 1/4, x² + 5y² + 4xy = 1/4, and the family of the ellipses centered at the origin that, at four different points, are tangent to these circles and to the upper and lower edges of the convex hull, using analytic geometry and implicit derivation.