On Central Collineations which Transform a Given Conic to a Circle

Sa？etak 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