## Is a cone the degenerate of a 4 dimensional hyperbola?

Is a cone a the degenerate of a 4 dimensional hyperbola?

I only ask because I think it is and I am not sure. I am trying to get better at higher dimensional visualizations.

My analogy being that a point is the degenerate of a 3 dimensional cone. With that logic wouldn't that make a cone the degenerate of a 4 dimensional hyperbola?
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 Sort of, though not 4 dimensions, but 3. x^2+y^2-z^2=C is a hyperboloid of two sheets if C<0, one sheet if C>0, and a cone when C=0.
 Aren't degenerates usually at least one dimension less than what they degenerate from? and If not could it still be the degenerate of a 4 dimensional hyperbola? Because I don't think a cone can exist in 4 dimensions, it would be too many axes going through a single point, right?

 Tags cone, degenerate, higher dimensions, hyperbola

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