Intersection of Plane and Implicit Surface

Hi everyone -

Is possible to obtain the *equation* of the curve that is created by
the intersection of a plane (the plane need not be infinite, just
rectangular), and and an implicit surface e.g. an elliptic paraboloid:
z = (x^2/a^2) + (y^2/b^2) . I've searched the net but 'haven't found
anything on the subject.

Thanks,

- Olumide