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!
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.