It would'v been a lot easier if we were able to express the function explicitly, but since it cant be expressed explicitly, we must parameterize it and in this case parameterization takes the following form
x=sqrt(1+z^2)*cos(phi)
y=sqrt(1+z^2)*sin(phi)
once you are done with parameterization, you can plot it like shown below:
[phi, Z] = meshgrid((0:0.1:2)*pi, (-2:0.1:2));
X=sqrt(1+Z.^2).*cos(phi);
Y=sqrt(1+Z.^2).*sin(phi);
surf(X, Y, Z);
