How to find general solution (in terms of parameters) for diophantine equations $x^2+y^2-z^2=1$ and $x^2+y^2-z^2=-1$?

It's easy to find such solutions for $x^2+y^2-z^2=0$ or $x^2+y^2-z^2-w^2=0$ or $x^2+y^2+z^2-w^2=0$, but for these ones I cannot find anything relevant.