 .The standard form of a noncentral conicoid is ax^{2} + by^{2} + 2wz + d = 0.
If w = 0, the equation represents a cylinder or a pair of straight lines. If w ≠ 0, the surface represented by the equation is called a paraboloid.
 The standard equation of a paraboloid is ax^{2} + by^{2} = 2wz, w ≠ 0
. There are two types of paraboloids. When a and b are of the same signs we get an elliptic paraboloid. When a and b are of opposite signs we get a hyperbolic paraboloid.
 The condition for a line with direction ratios α, β, γ to be a tangent to the central conicoid ax^{2}+ by^{2} = 2z at (x_{0}, y_{0}, z_{0}) is ax_{0}α +by_{0}β = γ.
 The equation of the tangent plane to the paraboloid ax^{2} + by^{2} = 2z at a point (x_{0}, y_{0}, z_{0}) is axx_{0} + byy_{0} = (z+z_{0}).
 The condition that the plane ux+vy+wz = p is a tangent plane to the paraboloid ax^{2} + by^{2} = 2z is
u^{2}/a + v^{2}/b + 2wp = 0.
 The planar section of a paraboloid is a conic section.
