Hello, Frostking!

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: .