A Constructive Algorithm for Transforming Conics in a Circle on Imaginary Laguerre Points

Abstract

The article is devoted to the consideration of the properties of Laguerre points in their constructive relationship with the solution of the problem of transforming a pair of conical curves into two circles. Geometric schemes are presented that reveal the principle of specifying a collinear transformation that establishes a correspondence between conics and their images in the form of circles, including if the Laguerre points defining this transformation are imaginary. In the solution of the problem, a geometric scheme for the formation of the main conjugations of conics is given, one of which is a circle. The conclusion is substantiated that the radical axis of the bundle of circles is a circle that has split into a pair of straight lines, one of which is infinitely distant. An algorithm for the formation of a series of elliptic curves induced by Laguerre points is presented.