Solving a quadratic in two variables

[zzmanzz]

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]

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 $x$.

 

[zzmanzz]

Ahh makes sense.. so the new A,B, C terms will have X, X² in it.. but that's ok since I have the other coefficients. Thanks!

 

[member 587159]

What do you exactly mean by solve for y?