Hyperbolic plane! You mean complex plane. Note is the circle while is the line .
sorry im rubbish i meant hyperbolic lines, ok so if i take what you said would i just substitute x=0 to get the intersection. i get confused as to how you get the circle from |z+2|=4
z=x+iy
| x+iy + 2|=4 group real and imaginary parts then mod
sqrt( ((x+2)^2) + (iy)^2)=4
and so on..
to get
((x+2)^2) - y^2 =16
where am i going wrong