Thank you, mathman!
I agree, I was thinking about the ambiguity as well. I could also choose v = x etc and this will lead to a different solution.
I do not understand, however, what else do I need to know about the problem to make it concrete?
Can you please help me with the following problem:
Given a function of the form f(x,y) = (a-b x)^2 - (c - d y)^2, how can I tell how does f change when (x-y) change?