Based on the discussion of circles, you might guess that the definition of a parabola will take the form: “The set of all points that...” and you would be correct. But the definition of a parabola is more complicated than that of a circle.

**Definition of a Parabola**

Take a point (called the *focus*) and a horizontal line (the *directrix)* that does not contain that point. The set of all points in a plane that are the *same distance from the focus as from the directrix* forms a parabola.

In the text, you begin with a specific example of this process. The focus is (0,3) and the directrix is the line

The resulting shape looks something like this:

You may recall that a circle is entirely defined by its center—but the center is not, itself, a part of the circle. In a similar way, the focus and directrix *define* a parabola; but neither the focus, nor any point on the directrix, is a *part* of the parabola. The vertex, on the other hand—the point located directly between the focus and the directrix—is a part of the parabola.

One of the obvious questions you might ask at this point is—who cares? It’s pretty obvious that circles come up a lot in the real world, but parabolas? It turns out that parabolas are more useful than you might think. For instance, many telescopes are based on parabolic mirrors. The reason is that all the light that comes in bounces off the mirror to the focus. The focus therefore becomes a point where you can see very dim, distant objects.

Comments:"DAISY and BRF versions of this collection are available."