Draw Circles and Tangents on a TI83 Plus Graph
The steps for drawing a circle on a graph with the TI83 Plus graphing calculator are similar to drawing a line segment on the graph. Press [2nd][PRGM][9] to select the Circle option from the Draw menu, place the cursor at the center of the circle and press [ENTER], then move the cursor to a point that defines the radius of the circle and press [ENTER].
Repeat this process to draw another circle or press [CLEAR] when you’re finished drawing circles.
Alternatively, if you know the center and radius of the circle, press [2nd][MODE] to exit the graph. Then press [2nd][PRGM][9]. Enter the center and radius of the circle, separated by commas, and then press [ ) ][ENTER].
You can draw a tangent line on the graph of a function, parametric equation, or polar equation. If you’re drawing a tangent to a function, as a bonus, the calculator gives you the equation of that tangent. If you’re drawing a tangent to a parametric or polar graph, the calculator will give you the slope of that tangent. To draw a tangent, follow these steps:

Set the Format menu to ExprOn and CoordOn and graph the functions, parametric equations, or polar equations.

Press [2nd][PRGM][5] to select the Tangent option from the Draw menu.

If necessary, repeatedly press
until the cursor is on the appropriate graph.

Use the
keys to move the cursor to the location of the tangent line and press [ENTER].
Instead of using the
keys, you can use the keypad to enter the precise location of the tangent. To do so, enter the value of the independent variable, and then press [ENTER].