This demo displays the curve X(t) that you can alter in the
appropriately labeled textbox, the point (x0, y0) that you can move by
clicking and dragging, a segment with endpoints (x0, y0) and X(t0), and
a graph of the length of the segment with endpoints (x0, y0) and X(t)
as a function of t.

To move X(t_{0}) along the curve, use the following keys on the
appropriate line in the control window:

[<]: Decrease t_{0}_{} by one step.

[>]: Increase t_{0} by one step.

[<<]: Decrease t_{0} until it reaches its minimum value.

[>>]: Increase t_{0} until it reaches its maximum value.

By default, the demo shows the point tracing out the curve, so that
only part of it is shown. To show the entire curve, check the box "Show
entire curve" by clicking on it. Click on the "Show position vector X(t_{0})"
box to show the position vector X(t_{0}) whose components
are the coordinates of the point X(t_{0}).