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.

Answerthe simplified expression isexplanationthe given expression is,let us deal with the bracket first.the two negatives in the parenthesis will become positive.the expression now becomes,we now expand the parenthesis to get,we group like terms to obtain,this simplifies to,

Ithink it's the first one ( let me know if it right)