Parameterization of a curve

 Objective:

Transform the function of a curve into parametric equations.

Parameterization of a curve

In the previous lesson we learn how to eliminate the parameter in the parametric equations of a curve. In this post we do the reverse meaning transforming a function of a curve into parametric equations.

Example

Find two different pairs of parametric equations to represent the graph of y = 2x² - 3

Solution

One of the easiest way to do this is to write x(t) = t and substitute x in the function. The result is y = 2 t²-3.

The first set of pair of parametric equations is x(t) = t y = 2t²-3

Since there is no restriction on the domain of the function, we can have a variety of expressions of x in function of t and then substitute x in the function.

For the second pair of equations let's choose x(t) = 3t-2

Let's substitute x in the function:

 

Therefore a second parameterization of the function is represented by:

Practice

Find two different sets of parametric equations to represent the graph of y = x² + 2x