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I have a system of two quadratic equations with unknowns $x$ and $y$:

$$a_{1 1} x y + a_{1 2} x^2 + a_{1 3} y^2 + a_{1 4} x + a_{1 5} y + a_{1 6} = 0,\\ a_{2 1} x y + a_{2 2} x^2 + a_{2 3} y^2 + a_{2 4} x + a_{2 5} y + a_{2 6} = 0,$$

where $a_{i j}$ are arbitrary scalars.

Is there an algebraic solution of the above system?

  • 1
    easy case would be ,if we could complete square in each equation,get similar to circle equation2012-07-26
  • 0
    So you have two [conic sections](http://en.wikipedia.org/wiki/Conic_section#Cartesian_coordinates) that cut each other and you are looking for the cut points?2012-07-26
  • 0
    Yes, I have tho conics and I am looking for the intersercion points.2012-07-26

2 Answers 2