Quadratic Surfaces
Ellipsoid:
1
x2 y 2 z 2
+ 2 + 2 =1
a2
b
c
Hyperboloid of two sheets:
x2 y 2 z 2
+ 2 − 2 = −1
a2
b
c
Hyperboloid of one sheet:
x2 y 2 z 2
+ 2 − 2 =1
a2
b
c
Elliptic cone:
x2 y 2
z2
+
=
a2
b2
c2
Quadratic Surfaces
Elliptic paraboloid:
2
z = ax2 + by 2
Hyperbolic paraboloid:
z = by 2 − ax2