Parametric cusp --- Introduction ---

Recall. A cusp of a plane parametric curve

x = f (t) , y = g(t)

is a singular point for a value t0 of t, characterized by the simultaneous conditions

f '(t0) = g '(t0) = 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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