Find a generating curve and the axis for the given surface of revolution

Surface : x^2 + y^2 - z^2 = 4

I'm not sure what I'm doing with this...

I get that a surface can be created by rotating a generating curve (or plane curve so to speak) about an axis.

I'm not sure how to go from 3d to 2d though (so as to find this curve from the surface)

When I look at the given surface I'm not too sure what's going on, so perhaps that's the problem?

I have x^2 + y^2 = z^2 + 4 , (after rearranging)

And i need to get this down to two variables, but what would indicate which axis was being rotated about?

And how would I go about choosing / finding which plane this surface created a generating curve in?

Thanks