Prove that rule for surface of revolution is of given value

Question

If we take take a curve z = f(y) in the yz-plane and revolve it about the z-axis, we obtain a surface of revolution in space. What do the level curves look like? Prove that the rule for the surface of revolution thus obtained is z= f(√(x² + y²)). Use this result to deduce that the equation x²+ y²+ 2x + 2y - z²+ 2 = 0 defines a cone in space.