# Sum of distances to foci is constant gives an ellipse

- Author:
- Kevin Weaver, Irina Boyadzhiev

- Topic:
- Ellipse

The applet demonstrates the following:

*An ellipse is the set of all points in the plane, the sum of whose distances to two fixed points (foci) remains constant.*- Select the length of a piece of string by dragging the endpoints of the blue segment.
- Drag the
**orange**point to select the position of the focus F1 along**the x-Axis or the y-Axis**. The other focus F2 is symmetrical to F1 with respect to the origin.

- Drag the tip of the pencil or press the “Draw” button to trace all points on the plane that satisfy the above definition.
- Hide the pencil by pressing the "Pencil ON/OFF" button; show the ellipse by pressing “Show Ellipse” button, and explore the curve by changing the positions of the foci and the length of the constructing string.
- Bring the two foci to the origin to see the circle as a special case of the ellipse.
- Click on “Labels” to see some terminology.