The picture shows an elliptic paraboloid with its curvature lines. These lines are the curves of intersection with confocal elliptic and hyperbolic paraboloids, and therefore, in general of degree four. Families of quadrics which intersect the planes of symmetry along confocal conics are called confocal. They belong to a range, i.e., a dual pencil. It is interesting to see that confocal quadrics are connected with various geometric problems, and often the famous theorem of Ivory plays a central role.
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