Find the equation of the sphere with points P such that the distance from P to A is twice the distance from P to B. A(-3, 6, 4), B(6, 2, -2) Solution Let P=(x,y,z) PA = distance between P and A =sqrt[ (x+3)^2 + (y-6)^2 + (z-4)^2 ] PB= distance between P and B = sqrt [ (x-6)^2 + (y-2)^2 + (z+2)^2 ] PA = 2*PB sqrt [ (x+3)^2 + (y-6)^2 + (z-4)^2 ] = 2*sqrt [ (x-6)^2 + (y-2)^2 + (z+2)^2 ] square both sides: (x+3)^2 + (y-6)^2 + (z-4)^2 = 4[(x-6)^2 + (y-2)^2 + (z+2)^2].