Original scientific paper

On the Focal Curve of Conic Pencils in I_2

Jelena Beban-Brkić ; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia

Abstract

Within the classification of conic pencils in the isotropic plane, which has been carried out using methods of analytical geometry and linear algebra, it is specially interesting to observe the curve of isotropic focuses, which is shown to be a 3rd order curve. The properties of this very curve for the discussed, most common subtype of conic pencils, are determined. It is shown that, referring to the selection of the fundamental points, it is possible to determine its shape, and to classify it according to the Newton's principle.
The discussed cases of conic pencils with its focal curves are illustrated with the figures drawn by Mathematica®.

Keywords

isotropic plane; fundamental points; pencil of conic sections; matrix of quadratic form; eigenvalues; focal curve; Newton's classification

Hrčak ID:

166350

URI

https://hrcak.srce.hr/166350

Publication date:

20.1.1998.

Article data in other languages: croatian

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