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Create a 3D Conic Section with Slice Through It

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Create a 3D Conic Section with Slice Through It

I would like to create an image similar to what is commonly depicted in math textbooks when introducing the conic sections: a right cone with cutting planes going through it at angles to show how the ellipse, circle, parabola, and hyperbola are created. Something similar to what is shown on the following Wikipedia page:

http://en.wikipedia.org/w/index.php?title=File:Conic_sections_with_plane.svg&page=1

For my purposes, I would presently just like to create an image of the bottom half of the double-cone, with an inclined cutting plane going through the cone to illustrate how an ellipse is created.

I assume I would

(i) input an equation such as y = 20 - 2x to create a line,

(ii) revolve this line around the y-axis to create a solid of revolution, and

(iii) create a cutting plane to cut through this solid of revolution at an angle.

Unfortunately, I don't know how to do this. Or I may be going down the wrong path in the first place.

How do I create a 3D Cone with cutting plane going through it at an angle to show an ellipse?

Your direction is appreciated.

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