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 non-degenerate if
main conics page