%0 Journal Article
%T On Central Collineations which Transform a Given Conic to a Circle
%A Gorjanc
%A Sonja
%A Hoffmann
%A Mikl¨®s
%A Schwarcz
%A Tibor
%J -
%D 2010
%X SaŁżetak In this paper we prove that for a given axis the centers of all central collineations which transform a given proper conic c into a circle, lie on one conic cc confocal to the original one. The conics c and cc intersect into real points and their common diametral chord is conjugate to the direction of the given axis. Furthermore, for a given center S the axes of all central collineations that transform conic c into a circle form two pencils of parallel lines. The directions of these pencils are conjugate to two common diametral chords of c and the confocal conic through S that cuts c at real points. Finally, we formulate a theorem about the connection of the pair of confocal conics and the fundamental elements of central collineations that transform these conics into circles
%K central collineation
%K confocal conics
%K Apollonian circles
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=94163