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From: leeper@mtgzz.UUCP (m.r.leeper)
Newsgroups: net.math
Subject: Foci of ellipses
Message-ID: <1605@mtgzz.UUCP>
Date: Sun, 26-Jan-86 06:43:31 EST
Article-I.D.: mtgzz.1605
Posted: Sun Jan 26 06:43:31 1986
Date-Received: Sun, 26-Jan-86 20:24:56 EST
Organization: AT&T Information Systems Labs, Holmdel NJ
Lines: 15

I have reason to believe this posting did not get to some systems.
I am reposting it:

This is kind of a nice, simple problem that I posed for myself and
solved.  The solution is kind of pleasing too.  In a three-space
(coordinates x, y and z) you have a cylinder whose equation is x^2 +
z^2 = 1.  Now if you take planes through the z-axis, each (but for the
one containing the y-axis) will intersect the cylinder in an ellipse.
Describe the locus of points that are foci of those elipses.  What
kind of a curve in three-space will the foci trace out as the angle of
the plane changes?  Express the solution in each of rectangular and
polar-coordinates, each is interesting.

				Mark Leeper
				...ihnp4!mtgzz!leeper