View source for Paraboloid

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A non-closed non-central [[Surface of the second order|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|elliptic paraboloid]], and

$$ 

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

for a [[Hyperbolic paraboloid|hyperbolic paraboloid]].

====Comments====

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,   "Geometry" , '''II''' , Springer  (1987)  pp. Chapt. 15</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  D. Pedoe,   "Geometry" , Dover, reprint  (1988)  pp. 135, 398</TD></TR></table>