Parametric cusp --- Introduction ---

A cusp of a plane parametric curve
x=f(t),y=g(t)
is a singular point for a value t 0 of t, characterized by the simultaneous conditions
f′(t 0)=g′(t 0)=0.
In this exercise, your goal is either to find a cusp in a given parametric curve, or to determine the parametric curve having a given cusp. This exercise accepts several configuration parameters which determine the aspect and the level of difficulty of the problem asked.
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