How to Graph Several Parametric Equations on the TI83 Plus
To identify the graphs of several pairs of parametric equations, set a different graph style for each pair of parametric equations on the TI83 Plus graphing calculator. The following steps show how:

Press [Y=] to access the Y= editor.

Use the
keys to place the cursor on the icon appearing at the very left of the definition of the first parametric equation in the pair of parametric equations.

Repeatedly press [ENTER] until you get the desired graph style.
You have five styles to choose from: Line, Thick Line, Path, Animate, and Dotted Line. Each time you press [ENTER], you get a different style. The Path style uses a circle to indicate a point as it’s being graphed, and when the graph is complete, the circle disappears and leaves the graph in Line style.
The Animate style also uses a circle to indicate a point as it’s being graphed, but when the graph is complete, no graph appears onscreen.
The most common styles used to graph parametric equations are Line, Thick Line, and Dotted Line.
If you don’t want the calculator to graph a pair of parametric equations, unhighlight the equal signs in that pair. To graph it at a later time, rehighlight the equal signs. You can do so in the Y= editor by using the
keys to place the cursor on the equal sign in the definition of either parametric equation in the pair, and then pressing [ENTER] to toggle the equal sign between highlighted and unhighlighted.