Gfind an equation of the sphere with points p such that the distance from p to a(−2, 4, 3) is twice the distance from p to b(6, 2, −2).

I'll help you get started.  

The distance from p to b(6,2, -2) is sqrt( (x-6)^2 + (y-2)^2 + (z+2)^2 )
and that from p to a is sqrt ( (x+2)^2 + (y-4)^2 + (z-3)^2 )

"the distance from p to a(−2, 4, 3) is twice the distance from p to b(6, 2, −2)"

translates into  

2 [ sqrt( (x-6)^2 + (y-2)^2 + (z+2)^2 ) ] = sqrt ( (x+2)^2 + (y-4)^2 + (z-3)^2 )

Square both sides.  Do all the indicated squaring.  Combine like terms.  Your answer must be in the form

     (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2, where r is the radius of the sphere and (x,y,z) represents a point on the surface of the sphere.

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