# Solving a quadratic in two variables

## 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.

Ray Vickson
Science Advisor
Homework Helper
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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##.

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!

member 587159
What do you exactly mean by solve for y?