1. The graph of f is a paraboloid

2. The intersection of the paraboloid with a plane parallel to the axis of the paraboloid must be a parabola.

3. Use parametric equation to get the intersection parabola:

4. I've attached a drawing of f and the cutting plane. Because it is very difficult to detect the parabola in this drawing I've sketched the parabola alone in a separate coordinate system.