Plotting a parabola. Geometric definition

A try square slides along the static ruler so that its hori­zontal leg touches the ruler.

One end of a thread is pinned to the try square’s vertex that is not lying on the ruler, another one is pinned to the sheet of paper. A pencil presses the thread to the triangle’s leg so that it remains stretched.

Let the thread be as long as triangle’s vertical leg (arbi­trary case can be reduced to this one). Press the thread to the triangle with a pencil, wind it around the pencil and fix its end near the try square with a pin. By that, the lead is the midpoint between the pin and the ruler.

As the try square slides, the lead remains equidis­tant from the ruler and the pin. That means, according to the geometric defi­n­i­tion, the lead will draw a parabola on paper with the pin being parabola’s focus and the ruler being its direc­trix.