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Solving a quadratic in two variables

  • Thread starter zzmanzz
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  • #1
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Homework Statement



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.
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement



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.
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##.
 
  • #3
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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!
 
  • #4
Math_QED
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What do you exactly mean by solve for y?
 

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