二次曲面有12种。以下是其名称及标准方程。
(1)圆柱面(Cyindrical surface)
x^2+y^2=a^2
(2)椭圆柱面(Elliptic cylinder)
x^2/a^2+y^2/b^2=1
(3)双曲柱面(Hyperbolic cylinder)
x^2/a^2-y^2/b^2=1
(4)抛物柱面(Parabolic cylinder)
y^2-2ax=0
(5)圆锥面(Conical surface)
(x^2+y^2)/a^2-z^2/c^2=0
(6)椭圆锥面(Elliptic cone)
x^2/a^2+y^2/b^2-z^2/c^2=0
(7)球面(Sphherical surface)
x^2+y^2+z^2=a^2
(8)椭球面(Ellipsoid)
x^2/a^2+y^2/b^2+z^2/c^2=1
(9)椭圆抛物面(Elliptic paraboloid)
x^2/a^2+y^2/b^2=z
(10)单叶双曲面(Hyperboloid of one sheet)
x^2/a^2+y^2/b^2-z^2/c^2=1
(11)双叶双曲面(Hyperboloid of two sheets)
x^2/a^2-y^2/b^2-z^2/c^2=1
(12)双曲抛物面(马鞍面)(Hyperbolic paraboloid)
x^2/a^2-y^2/b^2=z。
