We use a trick to let the trace "open up" as you drag a point.
The trick is this: an initial point is given parametric location s*t, create a tangent at this point and its envelope as s varies.
Now hide the original point and create another point with parameter t, and make it draggable.
Dragging the new point changes the value of t and we see a trace from 0 to t.
Tags: parabola, envelope