One-Sheeted- Hyperboloid

Question

I am given the following surface:

$z^2-xy=1$ . How can I show it is of the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2}=1$ ?

I can't find an appropriate coordinate change...

Will you help ?

Thanks a lot

Answer 1

Hint: Try letting $u=x+y$ and $v=x-y,$ and see if you can rewrite $z^2-xy=1$ in the form $$-\frac{u^2}{a^2}+\frac{v^2}{b^2}+\frac{z^2}{c^2}=1.$$