Finding the Center and Radius of a Sphere with Parallel Tangent Planes

[math12345]

A sphere has two parallel tangent planes with equations x+2y-2z=37 and x+2y-2z=-11. One of the points of tangency is (-7,5,7). Find the center and radius of the sphere.


I'm not really sure how to do this. I know that the point (-7,5,7) lies on the x+2y-2z=-11 plane. The distance from the point to the plane using the distance formula is 16. So now I know that the sphere's diameter is 16, making the radius 8.

Can someone explain how to find the center of the sphere?

Thanks!

 

[Dick]

That's good so far. Now find the normal direction of the planes. That means the center of the sphere lies 8 units in the direction of the normal from (-7,5,7) towards the other plane.