10.5- Parametric Equations

Parametric Equations

Parametric equations are used when a third variable is necessary to help graph an equation. This variable, called the parameter, is called T. T often represents time and angle measurement.

Eliminating the Parameter

When using parametric equations, the equation is often given in two parts, one solved for x and the other for y. When this is the case, it is best to plug in the x equation into the y equation.

 x=T+5

This creates an equation in terms of just x and y, and it can be used like a normal two variable graph, which is called a rectangular equation. This is a situation where T represents time.

You use a similar method when T represents an angle measure.

In this situation, you solve for sin and cos. You can than use the trigonometric identities to set up an equation:

 Using this rectangular equation, you can tell that this graph will form an ellipse with a center at the origin, x-intercepts at (-2,0) and (2,0), and y-intercepts at (0,-3) and (0,3).

Using a Graphing Calculator

A graphing calculator is an extremely useful tool for parametric equations. To change modes, go to mode-parametric. You will also want your calculator set to radian mode. You may also want to adjust your mode from sequential to simultaneous (Mode-Simul). This is useful when T represents time and you want to see if two things would intersect.