Definitions Given a point O, a line L through O, and αε(0,π/2), the cone with vertex O, axis L and angle α consists of all points on lines through O making angle α with L. The lines are called the generators of the cone.
As an example, take the origin O as vertex,


Intersections with planes not through the vertex are the usual plane conics.
Note. It is far from clear that these are conics


Intersections with planes through the vertex give degenerate plane conics.
Observe that each is either finite (a single point!), Theorem A plane conic is nondegenerate if

