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.
Change the value of t0 as in earlier demos.
As in earlier demos, there are "Show entire curve", "Show position vector X(t0)" and "Show Color Spectrum" options. "Show Color Spectrum" will also color the segment from (x0,y0) to X(t0), and the graph of this distance.