Hyperbolic Paraboloid as a Ruled Surface

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Translating and rotating a straight line generates a hyperbolic paraboloid. Therefore, it is a ruled surface, that is, there is a line on the surface through any given point; in fact there are two lines through each point. The intersection of the surface and a horizontal plane is a hyperbola.
Contributed by: Ferenc Holló Szabó and Sándor Kabai (April 2012)
Open content licensed under CC BY-NC-SA
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"Hyperbolic Paraboloid as a Ruled Surface"
http://demonstrations.wolfram.com/HyperbolicParaboloidAsARuledSurface/
Wolfram Demonstrations Project
Published: April 27 2012