Quadrics

sphere x 2 + y 2 + z 2 = r 2

hyperboloid of one sheet

cone

x2 y2 z 2
+
−
=1
a 2 b2 c2

x2 y2 z 2
+
−
=0
a 2 b2 c 2

ellipsoid

x2 y 2 z 2
+
+
=1
a 2 b2 c 2

hyperboloid of two sheets

elliptic paraboloid

x2 y2 z 2
−
−
=1
a2 b2 c2

x2 y2
+
=z
a2 b2