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So I'm doing some independent study and I'm at a loss for this problem.

1. The problem statement, all variables and given/known data

Let's say we have an ellipse of the form (x^{2})/a + (y^{2})/b = 1 which we obtain by slicing a plane through a right circular cone with an opening angle of [itex]\theta[/itex] (a fixed constant). We know the angle the plane makes with the xy-plane to be [itex]\phi[/itex]. We also know the cut crosses the center line of the cone at height h. In terms of h and [itex]\phi[/itex], what is a and b?

2. Relevant equations

I found this page that seemed to be pointing me in the right direction, but I can't make much sense of it:

http://www.physicsinsights.org/conic_sections_1.html

Also, the equation of the ellipse they are using is related to the foci of the ellipse which I don't know how to relate to the equation of an ellipse I'm looking for.

3. The attempt at a solution

I'm honestly not sure where to start or if this is possible. It seems to me like it should be, so any help would be greatly appreciated.

Thank you,

-anomie

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# Finding an ellipse from a plane slicing a cone

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