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