二次曲面有12種。以下是其名稱及標準方程。

(1)圓柱面(Cyindrical surface)

x^2+y^2=a^2

(2)橢圓柱面(Elliptic cylinder)

x^2/a^2+y^2/b^2=1

(3)雙曲柱面(Hyperbolic cylinder)

x^2/a^2-y^2/b^2=1

(4)拋物柱面(Parabolic cylinder)

y^2-2ax=0

(5)圓錐面(Conical surface)

(x^2+y^2)/a^2-z^2/c^2=0

(6)橢圓錐面(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)橢球面(Ellipsoid)

x^2/a^2+y^2/b^2+z^2/c^2=1

(9)橢圓拋物面(Elliptic paraboloid)

x^2/a^2+y^2/b^2=z

(10)單葉雙曲面(Hyperboloid of one sheet)

x^2/a^2+y^2/b^2-z^2/c^2=1

(11)雙葉雙曲面(Hyperboloid of two sheets)

x^2/a^2-y^2/b^2-z^2/c^2=1

(12)雙曲拋物面(馬鞍面)(Hyperbolic paraboloid)

x^2/a^2-y^2/b^2=z