engleski

On Central Collineations which Transform a Given Conic to a Circle

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.

{;central collineation; confocal conics; Apollonian circles

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