Paraboloid

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.

References

[a1]	M. Berger, "Geometry" , II , Springer (1987) pp. Chapt. 15
[a2]	D. Pedoe, "Geometry" , Dover, reprint (1988) pp. 135, 398