Ellipse from two foci and point
This applet shows an ellipse made from two foci and a point on the ellipse. Notice that as you move point P around, the sum of the lengths of the two dashed red segments is constant. Physically, you can make an ellipse with two pushpins (at the foci) and a piece of string tied to each foci. Here's an example: http://www.youtube.com/watch?v=7UD8hOs-vaI.
To change the shape of the ellipse, you can move the foci, as well as the small blue point.