Plane parallel to the circular base not passing through the tip of the cone

Question

And and the table describe the shape of the cross-section formed when are particular plane passes through the cone

Answer 1

Hi Kenny E.,

Still a circle. Try to find a kids' birthday party hat, the kind that's a little cone with an elastic band, to visualize. If the slice is between parallel-to-the-base and at-the-cone-angle, then it will cut an ellipse (one side only). Parallel to the cone axis, makes two parabolas; crossing the cone axis makes hyperbolas (I think).

-- Cheers, -- Mr. d.

P.S. the fun comes when you look at the equations for each of these; you'll get into that next, perhaps.