This applet walks through the sum of distances constructions of an
ellipse.
In that definition, an ellipse is the set of all points from which the
sum of the distances to the two
foci is a fixed number.
Once the ellipse is constructed, the foci and the fixed distance can be changed by dragging the points.
Created with GeoGebra.
GeoGebra is a GNUed software package for mathematics visualization. The home for this application is http://www.geogebra.org.