1. 1.4 Parametric Equations Mt. Washington Cog Railway, NH
Greg Kelly, Hanford High School, Richland, Washington
Photo by Greg Kelly, 2005

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. To graph on the TI-89: Graph……. 2 Y= WINDOW GRAPH Example 1: T ) MODE
ENTER
PARAMETRIC Y=
2nd T )
ENTER
WINDOW
GRAPH

4. Hit zoom square to see the correct, undistorted curve.
We can confirm this algebraically:
parabolic function

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

6. Graph on your calculator:
Use a [-4,4] x [-2,2]
window.
WINDOW
GRAPH

7. Ellipse:
This is the equation of an ellipse. p