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Intersection of Conic Sections

• To: mathgroup at smc.vnet.net
• Subject: [mg66277] Intersection of Conic Sections
• From: "irchans" <infinitgames at yahoo.com>
• Date: Sat, 6 May 2006 23:50:40 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

This seems like a simple question, but I am finding it diffucult to
find a simple solution.

What are the points of intersection of

0 = A1 + A2*x + A3*y + A4*x^2 + A5*x*y + A6*y^2

and

0 = B1 + B2*x + B3*y + B4*x^2 + B5*x*y + B6*y^2


where Ai and Bi are constants.

When I solve this with mathematica, I get a rather complex expression.
Is there a simple algorithm that finds all the roots?

Cheers,
Irchans

• Follow-Ups:
  • Re: Intersection of Conic Sections
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>