This is easier than you think . . .
Try to visualize the graph . . .Find the equation of a plane tangent to the sphere
that is parallel to the -plane
We have a sphere: center (4, -1, 3) and radius 2.
A plane parallel to the -plane is "horizontal" .
It would be tangent to the sphere at its "north pole" or "south pole."
The north pole is (4, -1, 5); the south pole is (4,-1, 1).
Hence, the tangent plane is either: .