Conics from symmetric Pythagorean triple preserving matrices

Abstract

The aim of this paper is to introduce and study the class of conics provided by symmetric Pythagorean triple preserving matrices. This class depends on three real parameters and various relationships between these parameters give special subclasses. A symmetric matrix of Barning and its associated hyperbola are carefully analyzed through a pair of points of rational coordinates. We transform and extend this latter hyperbola to a class of hyperbolas containing integral points (k; k + 3), (k + 3; k). A complex approach is also included.