If O is a fixed point and a variable point P moves along a fixed curve C, surface generated by the straight line OP is a cone. The fixed point O is called the vertex, C a base curve and OP a generator of the surface.    

• The general homogenous quadric equation in three variables x, y, z   where a, b, c, f, g, h are constants represents a cone, with its vertex at the origin.

• If the quantities l,m,n satisfy the relation

then the line whose direction cosines proportional to l,m,n is the generator of the cone.

• In equation  (1) if the expression on the left splits into two linear factors then (1) represents a pair of planes.  splits into two linear factors if   

• Equation (1) represents a cone if