How to Enter Parametric Equations on the TI83 Plus
The TI83 Plus graphing calculator can handle up to six pairs of parametric equations, X_{1T} and Y_{1T} through X_{6T} and Y_{6T}. To enter parametric equations in the calculator:

Press [MODE] and put the calculator in Parametric mode.
To highlight an item in the Mode menu, use the
keys to place the cursor on the item, and then press [ENTER]. Highlight Par in the fourth line to put the calculator in Parametric mode.

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

Enter the definitions of the pair of parametric equations X_{nT} and Y_{nT}, with n being an integer between 1 and 6.
To erase an entry that appears after X_{nT} or Y_{nT}, use the
keys to place the cursor to the right of the equal sign and press [CLEAR]. Then enter your definition for the new parametric equation.
When defining parametric equations, the only symbol the calculator allows for the independent variable (parameter) is the letter T. Press
to enter this letter in the definition of your parametric equation. Here, this key was used to enter the X_{1T} parametric equation.
As a time saving convenience, when entering a parametric equation in the Y= editor, you can reference another parametric equation in its definition. Equations Y_{1T}, X_{3T}, and Y_{3T} are defined in this manner. To paste a parametric equation name in the equation you’re entering in the Y= editor, press
and then press the number key for the name of the parametric equation you want pasted in the definition.
Parametric equations must be entered in pairs. If you enter just one equation in the pair, say X_{nT} but not Y_{nT}, then when you go to graph these parametric equations, you won’t see a graph nor will you get an error message warning you that there is a problem.