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