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.
