Area 'twixt an ellipse and the apex of a cone.

Frederick Williams · science forum addict Joined: 19 Nov 2005 Posts: 97

A plane cuts a cone in an ellipse. The distances from the apex to the
ends of the major axis are b, c. The angle of the apex is C. The area
of that part of the cone that lies between its apex and the ellipse is

A = pi (b + c)/2 sqrt(bc) sin(C/2).

I can prove this using Cartesian co-ordinates, but it would be nice to
have an intrinsic proof. Any thoughts?

--
Remove "antispam" and ".invalid" for e-mail address.

Google