what is cubic circle?????
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The circularcubics are the cubics passing by cyclic points. It can be proved that they are the cyclic curves for which the initial curve is a parabola. In other words, they are the envelopes of circles the centres of which describe a parabola, and such that a fixed point (the pole) has a constant power with respect to these circles (i.e. these circles have an orthogonal or pseudo-orthogonal intersection with a fixed circle, the directrix circle).
They are rational iff this power is zero.
A circular cubic can be obtained by four definitions of this type in the general case. It loses one if it has a symmetry axis. Independently, it loses two or three of these definitions when it is rational (depending on the kind of singularixty).
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