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Solving a quadratic in two variables

  1. May 23, 2016 #1
    1. The problem statement, all variables and given/known data

    Hi,

    If I have an equation in the form

    0 = a*x^2 + b*y^2 + c*x*y + d*x + e*y + c

    Is it possible to solve this for y? Was hoping just to get a helpful link as this isn't for homework - just a personal project.
     
  2. jcsd
  3. May 23, 2016 #2

    Ray Vickson

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    I assume you really mean ##0 = a x^2 + b y^2 + c x y + d x + e y + f##; that is, that the last term should not be ##c## as you wrote.

    Yes, you can easily solve for ##y## in terms of ##x##, because it is a quadratic equation of the form ##A y^2 + B y + C = 0##, where you can use algebra to figure out what are ##A, B## and ##C## in terms of ##a,b,c,d,e,f## and ##x##.
     
  4. May 23, 2016 #3
    Ahh makes sense.. so the new A,B, C terms will have X, X2 in it.. but thats ok since I have the other coefficients. Thanks!
     
  5. May 24, 2016 #4

    Math_QED

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    What do you exactly mean by solve for y?
     
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