 A general second degree equation in three variables is
ax^{2} + by^{2} + cz^{2} + 2fyz + 2gzx + 2gxy + 2ux + 2vy + 2wz + d = 0
 A conicoid or quadric surface in the three dimensional coordinate system is the set S of points (x, y, z) ∈ R^{3} that satisfies a general second degree equation in three variables.
 When a = b = c = 1 and f = g = h = 0 the equation represents a sphere.
 When u = v = w = d = 0 then the equation represents a cone.
 When a = b = 1, h = 0 and z = k then the equation represents a right circular cylinder.
 When x = k or y = k and a = b = 1, h = 0, then again the equation represents a cylinder.
 A conicoid remains a conicoid under the translation or rotation of axes.
