Professional paper

The Curve of Centres and the Curve of all Isotropic Focal points in the Conic Section pencil Given by Two Double points of an Isotropic Plane

Miljenko Lapaine orcid.org/0000-0002-9463-2329 ; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia

Abstract

Conic section pencils given by two double points are discussed. It is proved that the curve of centres decomposes into two straight lines, one of which is passing through the two double base points, while the other is passing through the intersection of common tanget lines of all conics of the pencil and through the centre of the straight segment joining the base points. Furthermore, it is proved that the curve of all isotropic focal points decomposes into a straight line and a conic. These straight line and conic are passing through the double base points of pencil, and the conic through the intersection of common tangent lines of all conics of the pencil.

Keywords

conic section pencil; curve of centres; curve of all isotropic focal points; isotropic plane

Hrčak ID:

3939

URI

https://hrcak.srce.hr/3939

Publication date:

17.2.2003.

Article data in other languages: croatian

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