Question

What are parametric equations used for?

Answer 1

Parametric equations are useful when a position of an object is described in terms of time `t`. Let us look at a couple of example.

Example 1 (2-D)

If a particle moves along a circular path of radius r centered at `(x_0,y_0)`, then its position at time `t` can be described by parametric equations like:

`{(x(t)=x_0+rcost),(y(t)=y_0+rsint):}`

Example 2 (3-D)

If a particle rises along a spiral path of radius r centered along the `z`-axis, then its position at time `t` can be described by parametric equations like:

`{(x(t)=rcost),(y(t)=rsint),(z(t)=t):}`

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.