The focus/directrix construction of a parabola

To see the steps of the construction, use the slider or the "play" button in the lower left of the window.
Point C moves the point E on the parabola.
Adjust the (apparent) shape of the parabola with points A, B, and C.

One definition of a parabola is: the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix.)
In this construction, you can see that distances are equal: the sides of the isosceles triangle ADE.

The parabola appears to be narrower the farther the focus is from the directrix. But is this just zooming out? Think about how this diagram can be used to prove that all parabolas are similar.

Susan Addington, Created with GeoGebra