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

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)

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

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

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

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

Ellipse: This is the equation of an ellipse. 