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Sphere/tangent planes?

by math12345
Tags: planes, sphere or tangent
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May15-11, 08:50 PM
P: 5
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?

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May15-11, 10:08 PM
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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.

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