The Parametric Equations Applet.

This applet allows you to graph 2-dimensional parametric curves.

We are assuming that a curve is given by <x(u),y(u)> with u running between u ini ... u fin;(see the bottom of the applet screen). The computer will display the curve by plotting it at number of points points and then connecting these points by straight lines. Clicking on the button Plot will produce the graph of the specified curve. 

The Constrained/Unconstrained button toggles between the two modes; it controls the scaling of graph. The current x and y coordinates of the mouse are displayed in the blue box in the lower left corner of the applet.

Finally,  as the graph is being drawn,  an arrow will appear indicating the direction and the magnitude of the tangent vector at the current point.
If your browser recognized the applet tag, you would see an applet here.