In this page, we show pictures of conics obtained as sections of a right circular cone. For completeness, we include the degenerate cases.
Definitions
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 The theorem of Dandelin shows this directly.
Here, we will show that the sections of a cone The equations of conic sections


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

