Plotting a parabola. Geometric definition

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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.