Your hyperbola equation is centred at (0,0) so you can restrict the domain as x>0 or x<0.
I know how to write the equation of a hyperbola with its two branches (i.e. x^2/a^2-y^2/b^2=1 or vice versa), but can you write the equation of just one branch of the hyperbola? Would it just be the equation of a parabola?
I know you could restrict the domain for those with horizontal transverse axes, but what about for vertical or in general?