A parabola is the set of all points equidistant
from a fixed line, called the * directrix*, and a fixed
point, called the

First we begin with the directrix, focus (point F) and some arbitrary point P on the directrix:

A point that is equidistant from the focus and P lies on the perpendicular bisector of segment FP:

Next, we can construct a perpendicular line to the directrix through P that will intersect the perpendicular bisector of segment FP:

If we construct the segment with the focus and the intersection of the two perpendiculars, an isosceles triangle is formed; therefore this point (point L) is equidistant from the focus F and the directrix.

Tracing point L as point P moves along the directrix creates the set of points that represents a parabola.

Notice that the perpendicular bisector of segment FP is tangent to the curve. If we trace this line, this will also create our parabola:

In Geometer's Sketchpad, the locus command
can also be used to generate the parabola. If point P and point
L are selected, the set of points is created by choosing "Locus"
from the **Construct menu:**