In the interactive model below, one end of a string is attached to rod NA at point N. The other end is tied to a nail at point F. The total length of the string is equal to NA.
The string is held taut against the rod by a pencil. Drag point A. The pencil will trace a path. To draw a new curve, move point F to a new location. Then click the red 'X' in the lower right corner to clear the existing trace. Draw the new curve by dragging point A again.
Can you prove that the path is a parabola? To do so, use the distance definition of a parabola: the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).