Hyperbola and circular cone

[tmoria]

Hi,

If one is given an equation that describes a hyperbola, is it possible to determine the aperture and slope of the cone it is a section of, or could it be a section of different cones?
I'm not interested in the height of the cone as the hyperbola and cone could be extended infinitely.

Thanks

 

[pappus]

Hi,

If one is given an equation that describes a hyperbola, is it possible to determine the aperture and slope of the cone it is a section of, or could it be a section of different cones?
I'm not interested in the height of the cone as the hyperbola and cone could be extended infinitely.

Thanks

I can't give you a solution. But maybe you can use Dandelin's spheres to answer your question.

http://www.komal.hu/cikkek/dandelin/dandelin.e.shtml

 

[tmoria]

I can't give you a solution. But maybe you can use Dandelin's spheres to answer your question.

http://www.komal.hu/cikkek/dandelin/dandelin.e.shtml

Thanks for the link. Not sure it is helpful but I'll study it more tomorrow.