4. Consider the surface S defined by $z = g(x, y) = ax^2 + 2y^2$.
(a) Find the tangent plane to S at the point $(3, 2, g(3, 2))$.
(b) (i) Find all values of a for which the tangent plane to the surface at $(x', y', z) \in S$
contains the point $(0, 0, -1)$.
(ii) Find all values of a for which the tangent plane to the surface at $(x', y', z) \in S$
contains the point $(-3, -2, 0)$.
(c)
(All steps in the calculations must be clearly shown.)