# Math Help - equation of a plane touching a sphere

1. ## equation of a plane touching a sphere

I need to find the equation for a plane that just touches a sphere (x - 4)^2 + (y + 1)^2 + (z - 3)^2 = 4 that is parallel to the xy plane

In writing this I think I would just set x and y to zero and solve for z and therefore z = 5 would be the answer. Could someone please confirm this for me??

So, if this were to be parallel to the zy plane then I would just solve for x with z and y at 0, Right? IN that case x would = 2

THanks so much for all the assistance you folks have provided, it really helps. Frostking

2. Hello, Frostking!

This is easier than you think . . .

Find the equation of a plane tangent to the sphere $(x - 4)^2 + (y + 1)^2 + (z - 3)^2 \:=\: 4$
that is parallel to the $xy$-plane
Try to visualize the graph . . .

We have a sphere: center (4, -1, 3) and radius 2.

A plane parallel to the $xy$-plane is "horizontal" . $(z \,=\,\text{constant}).$

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: . $z = 5\:\text{ or }\:z = 1$