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Sphere/tangent planes? 
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#1
May1511, 08:50 PM

P: 5

A sphere has two parallel tangent planes with equations x+2y2z=37 and x+2y2z=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+2y2z=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! 


#2
May1511, 10:08 PM

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Thanks
P: 25,228

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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