1. Parametric Equations Until now, we’ve been using x and y as variables. With parametric equations, they now become FUNCTIONS of a variable t.

2. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for the x and y coordinates in terms of a third variable (usually t or ). These are called parametric equations. “ t ” is the parameter. (It is also the independent variable)

3. Example Relations What does this look like in our non- parametric world?

4. Circle: If we let t = the angle, then: Since: We could identify the parametric equations as a circle.

5. Ellipse: This is the equation of an ellipse. 

6. Example Lines and Other Curves