What are parametric equations used for?
Parametric equations are useful when a position of an object is described in terms of time
Example 1 (2-D)
If a particle moves along a circular path of radius r centered at
Example 2 (3-D)
If a particle rises along a spiral path of radius r centered along the
Parametric equations are useful in these examples since they allow us to describe each coordinate of the position of a particle separately in terms of time.
I hope that this was helpful.