The polar form is {(u+p) cos 26} a+{(u-p) sin 20) a = (2k)t, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c =a or = oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed.
The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a node within the circle; the particular case when b= 2a is known as the trisectrix.
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