- #1
anomiet
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Hello,
So I'm doing some independent study and I'm at a loss for this problem.
Let's say we have an ellipse of the form (x2)/a + (y2)/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?
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.
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
So I'm doing some independent study and I'm at a loss for this problem.
Homework Statement
Let's say we have an ellipse of the form (x2)/a + (y2)/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?
Homework 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.
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