Sunday, April 19, 2015

On the Geometric Definition of 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. 

A string with the selected length is attached to both foci and is kept tight by the tip of the pencil.

  • 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.

Irina Boyadzhiev, April 19, 2015, Created with GeoGebra

Download applet
Irina Boyadzhiev's  GeoGebra Applets

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