Consider the surface S given by the equation $z^2 = x^2 - y$. The plane $13x + 8y + 11z - 33 = 0$ is parallel to the tangent plane to S at a point P $(x_0, y_0, z_0)$ in S.
Find the coordinates of P. (If an answer does not exist, enter DNE.)
$(x_0, y_0, z_0) = $