1.4 Parametric Equations. 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.

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1.4 Parametric Equations

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 with both x and y as variables dependent upon t )

Example 1: To graph on the TI-83: Note that the standard window setting has t going from 0 to 2  by default.

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: Now graph this on your calculator...don’t forget to hit Zoom-5. Write this in parametric form Try changing the radius

Ellipse: This is the equation of an ellipse. 