What are two steps for eliminating the parameter for parametric equations?

Answer 1

For this explanation, let's assume you have a curve that is parametrically defined by:

x=4t

y=t2+et

An easy way to "eliminate" the parameter and therefore have a function defined by variables x and y is to solve for t using one of the parameterized variables:

x=4t, so t=x/4

This solution for t can be plugged into the other parametrized variable:

y=t2+et and t=x/4, so y=(x/4)2+ex/4

y=x2/16+ex/4

You now have a single-variable function equivalent to the parameterized curve. This method does not always work, but for most general calculus classes (especially Calc I), this is all that you will need to know.