Find the Points on the Ellipsoid $x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = 7$

Essay

Find the points on the ellipsoid $x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = 7$ where the tangent plane is parallel to the plane $- 2 x + 2 y - z = 0$ .