Legitimate geometry question on cone-plane intersection

From	moroney@world.std.spaamtrap.com (Michael Moroney)
Newsgroups	sci.math
Subject	Legitimate geometry question on cone-plane intersection
Date	2019-01-05 17:48 +0000
Organization	The World : www.TheWorld.com : Since 1989
Message-ID	<q0qqlf$94n$1@pcls7.std.com> (permalink)
References	<17674064-528b-436c-abef-e44ddb32429d@googlegroups.com>

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I have a geometry question for anyone who knows geometry regarding the
cone-plane intersection ellipse. Given:

  
       /  \A 
   Y/  C  \X 
  B/         \ 
  

Since the angle AXC must be less than 90 degrees and the angle BYC must be
greater than 90 degrees and the length XC = YC, segment AC must be less
than BC. Therefore the center of the ellipse cannot correspond to the axis
of the cone, but AB is the major axis of the ellipse with point C lying on
the major axis.

Does point C correspond to one of the foci of the ellipse? If so, does
anyone know the name of a mathematical proof of this? If not, does point C
have a name, and what is the formula for finding the distance from the
center of the ellipse to the point C?

Thread

AP's thoughts as of 5JAN2019// three proofs that ellipse is never a conic Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 07:19 -0800
  Legitimate geometry question on cone-plane intersection moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-05 17:48 +0000
    Re: Legitimate geometry question on cone-plane intersection Alan Mackenzie <acm@muc.de> - 2019-01-05 18:58 +0000
      Re: Legitimate geometry question on cone-plane intersection moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-05 19:44 +0000
        Re: Legitimate geometry question on cone-plane intersection Peter Percival <peterxpercival@hotmail.com> - 2019-01-05 20:15 +0000
        Re: Legitimate geometry question on cone-plane intersection Alan Mackenzie <acm@muc.de> - 2019-01-07 03:15 +0000
          Re: Legitimate geometry question on cone-plane intersection moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-07 04:44 +0000
      Re: Legitimate geometry question on cone-plane intersection Peter Percival <peterxpercival@hotmail.com> - 2019-01-05 20:13 +0000
        My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 13:44 -0800
          try wrapping a ellipse in a cone wrapper Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 14:24 -0800
            Re: try wrapping a ellipse in a cone wrapper Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 14:40 -0800
              researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 17:37 -0800
                researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 21:13 -0800
                Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-06 05:55 +0000
                not even a constant percentage in the rectangles Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 21:59 -0800
                no percentage formula Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 22:14 -0800
                not even rectangles Re: no percentage formula Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 23:02 -0800
                directrix Re: not even rectangles Re: no percentage formula Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 23:34 -0800
                understanding the Ellipse well,is the same as understanding angular momentum of physics well Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 23:51 -0800
                Re: understanding the Ellipse well,is the same as understanding angular momentum of physics well Me <franz.fritschee.ff@gmail.com> - 2019-01-06 03:10 -0800
          Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Me <franz.fritschee.ff@gmail.com> - 2019-01-06 03:08 -0800
          Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Alan Mackenzie <acm@muc.de> - 2019-01-06 11:17 +0000
            Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-06 18:42 +0000
  Re: AP's thoughts as of 5JAN2019// three proofs that ellipse is never a conic Jan <filmart@gmail.com> - 2019-01-06 21:47 -0800

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