This page uses **JavaSketchpad**, a World-Wide-Web component of *The Geometer's Sketchpad.* Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.

####

LocusOfFocus

Point *X* projects onto line *AB* in point *X'*, and point *F* is the reflection of *X'* in *X*. The parabola having *F* as focus and *AB* as directrix is the locus of point *P*.
As *X* goes around a circle, the locus of the focus is an ellipse.

This configuration is of particular interest since the parabola is a function of *X* (quite different from "*y = x*^{2}", because here, as *X* varies, the whole parabola varies).

For more, see *GEOMETRY IN ACTION*, Chapter 2.