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On the Bicircular Quartic


     

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A fundamental theorem of the general bicircular quantic, given by Casey, is the following:-

A bicircular quartic can be generated in four and only four ways as the envelope of a circle which cuts a fixed circle orthogonally and whose centre moves on a fixed central conic. This fixed conic is called a focal conic and the four focal conies corresponding to the four methods of generating the quartic are confocal, their foci being the double foci of the quartic.


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  • On the Bicircular Quartic

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Abstract


A fundamental theorem of the general bicircular quantic, given by Casey, is the following:-

A bicircular quartic can be generated in four and only four ways as the envelope of a circle which cuts a fixed circle orthogonally and whose centre moves on a fixed central conic. This fixed conic is called a focal conic and the four focal conies corresponding to the four methods of generating the quartic are confocal, their foci being the double foci of the quartic.