Drag the red points!

First drag the directrix to the left and right; the program draws the point equidistant from the focus and the directrix. The lengths of the two red segments are equal. The locus (path) of all the points forms a parabola.

Next drag the focus. Watch what happens when it gets closer to or further from the directrix.

This is how parabolas have been drawn since the Ancient Greeks. Now we don't have to do it by hand!