Hyperbolic paraboloid

A non-closed non-central surface of the second order. In a suitable coordinate system (see Fig.) the equation of a hyperbolic paraboloid is

Sections of a hyperbolic paraboloid by planes parallel to the planes and are parabolas, while sections by planes parallel to the plane are hyperbolas (the section by the plane consists of two straight lines). The symmetry axis of a hyperbolic paraboloid is said to be its axis; the point of intersection of a hyperbolic paraboloid with the axis is known as the apex. If , the hyperbolic paraboloid has two axes of symmetry.

Figure: h048290a

A hyperbolic paraboloid is a ruled surface; the equations of the rectilinear generators passing through a given point have the form

References

[a1]	M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)
[a2]	D. Hilbert, S.E. Cohn-Vossen, "Geometry and the imagination" , Chelsea (1952) (Translated from German)