Intersection of Quadratic Surfaces or Conic Sections
Category: Science > Math
Asked by: infinitgames2-ga
List Price: $40.00
06 May 2006 07:49 PDT
Expires: 05 Jun 2006 07:49 PDT
Question ID: 726051
Write a computer program or solve algebraically for all the points of intersection (real and complex) of the two curves defined by 0 = A1 + A2*x + A3*y + A4*x^2 + A5*x*y + A6*y^2 0 = B1 + B2*x + B3*y + B4*x^2 + B5*x*y + B6*y^2 (References to correct solutions in the Literature would be appreciated, but are unnecessary.) where Ai and Bi are given constants.
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Re: Intersection of Quadratic Surfaces or Conic Sections
From: sgopal1-ga on 08 May 2006 14:10 PDT
I think i know how to solve for all the questions. First write the two euqations as a quadratic in y which would give A6*y^2+(A3+A5*x)*y+(A1+A2*x+A4*x^2)=0 B6*y^2+(B3+B5*x)*y+(B1+B2*x+B4*x^2)=0 If you then multiply each of these equations once with y and once with y^2 you can write it matrix, vey diffucult to write without equation editor. Then you convert this problem to a quadratic eigen value problem in x. To solve this quadratic eigenvalue proglem, perform first order realization and solve an eigenvalue problem using MATLAB. This would give you all the solutions of x, both real and complex. Once you have x you can solve for y. If you need details I can send you the word file that has all the details and the MATLAB code too.
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