your name: Brooke
the level of the question: 12
who is asking the question: Student
Which conic cannot be generated by an intersection of a plane and a double napped cone?
Hi Brooke,
There is some misunderstanding here. The official definition of a conic
since the time of the ancient Greeks:
a conic is the plane section of a cone.
I suppose one can define a conic the way it is done in algebra -- as
the graph of a second degree equation in x and y. This allows for
degenerate conics. In that case, one cannot get the "degenerate" conic x^{ 2} = 1 (consisting of a pair of parallel lines) as a section of a cone.
Chris