Find an equation of the sphere with points p such that the distance from p to a(−3, 6, 4) is twice the distance from p to b(5, 3, −2).

Find an equation of the sphere with points p such that the distance from p to a(-3, 6, 4) is twice the distance from p to b(5, 3, -2). Pa =2 pB Pa^2 = 4 Pb^2 (x + 3)^2 + (y - 6)^2 + (z - 4)^2 = 4( (x - 5)^2 + (y - 3)^2 + (z + 2)^2 ) x^2 + 6x + y^2 - 12y + z^2 - 8z + 61 = 4 x^2-40 x+4 y^2-24 y+4 z^2+16 z+152 3x^2 - 46x + 3y^2 - 12y + 3z^2 + 24z + 91 = 0 x^2 - (46/3) x + y^2 - 6y + z^2 + (24/3) z + 91/3 = 0 (x - 23/3)^2 + (y - 3)^2 + (z + 12/3)^2 = 529/9 + 9 + 144/9 - 91/3 (x - 23/3)^2 + (y - 3)^2 + (z + 12/3)^2 = 296/9 center = (23/3, 3, -12/3) radius = 53.43