This demo displays the circle given by rational parametrization X(t) = ((1 - t2)/(1 + t2), 2t/(1 + t2)). To move the point X(t0) along the line, use the following keys on the appropriate line in the control window:

Change the value of t0 as in earlier demos.
Check the box "Angle paramter" to see some geometric properties of this parametrization.

As in earlier demos, there are "Show entire curve", "Show position vector X(t0)" and "Show Color Spectrum" options.