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Confocal ellipses are ellipses sharing common foci (left figure). The nondegenerate members of the family cover the plane outside the closed line segment joining the foci, in the sense that there is a unique ellipse through each such point (Hilbert and Cohn-Vossen 1999, p. 5). The figure on the right shows confocal ellipses superimposed on confocal hyperbolas, which form an orthogonal net of curves (Hilbert and Cohn-Vossen 1999, pp. 5-6).
Graves's theorem gives a string construction of an outer ellipse confocal with a given ellipse.
