Ellipses sharing common foci (left figure). The family of confocal ellipses covers the plane simply, in the sense
that there is a unique ellipse passing through each point in the plane (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).
