This Demonstration constructs an ellipse with a Tusi couple. You can change the eccentricity of the ellipse and watch the changes in the vector elements used in its construction. You can also show the foci and the directrices of the ellipse.
Nasir al-Din al-Tusi, a thirteenth-century Persian mathematician, devised a technique to generate linear motion from the sum of two circular motions. Choosing an appropriate position of the generating point may produce other curves, such as the ellipse described in this Demonstration. Further details can be found in [1, 2].