You can find a general method for generating meshes from equations for 3D surfaces in the answers to this question.
In this instance you don't need the complexity of a parametric equation but you can easily find the equations for a paraboloid on Wikipedia. In this case, if you want to use the parametric form, $x = u$ and $y = v$ makes it easy enough to translate the basic equation to
$$ z = u^2 / a^2 + v^2 / b^2$$
and you can plug that math into the generic answer thusly:
I've pulled all of the parameters you might normally change into inputs. You could hook those to the Group Input node and control the parameters of the paraboloid from the modifier, if you wanted.
As a bonus for reading this far, here's the node group in a blend file so you don't have to reconstruct it.