Thread: finding solutions for a mixed variable equation

Hi there, this is a for a calculus question but it's more the algebra I'm having trouble with at the moment.
I've reduced an equation down to:

2y^2 + x^2 - 4xy + 4y - 4x = 0

and need to find all (x,y) pairs that make it true. Could someone show each step in solving this?
Thanks a lot

1) Did you encounter "Rotation of Axes" in your pre-calculus studies?

2) Without reference to the geometry, you can make a substitution that will solve the problem. and is one such substitution. You can then Complete the Square in u and in v and you'll ne much closer to a solution.

Hello, kiwi5!

. . Are you sure this is correct?
. ALL of them??

I'm quite certain that your equation is incorrect.

It represents a hyperbola . . . and hence has brizillions of solutions.

Originally Posted by kiwi5

Hi there, this is a for a calculus question but it's more the algebra I'm having trouble with at the moment.
I've reduced an equation down to:

2y^2 + x^2 - 4xy + 4y - 4x = 0

and need to find all (x,y) pairs that make it true. Could someone show each step in solving this?
Thanks a lot

you can look at it as a quadratic in . the equation becomes . now apply the formula for solving a quadratic and you will have found in terms of . that will do.