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Paraboloid

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A non-closed non-central surface of the second order. The canonical equations of a paraboloid are

$$ \frac{x ^ {2} }{p} + \frac{y ^ {2} }{q} = 2z,\ \ p, q > 0, $$

for an elliptic paraboloid, and

$$ \frac{x ^ {2} }{p} - \frac{y ^ {2} }{q} = 2z,\ \ p, q > 0, $$

for a hyperbolic paraboloid.

Comments

References

[a1] M. Berger, "Geometry" , II , Springer (1987) pp. Chapt. 15
[a2] D. Pedoe, "Geometry" , Dover, reprint (1988) pp. 135, 398
How to Cite This Entry:
Paraboloid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Paraboloid&oldid=14665
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article