Consider, C(0,y,0) point which lies on y axis and is equidistant from points A(3, 1, 2) and B(5, 5, 2).
∴ AC = BC
\(\sqrt{(0-3)^2+(y-1)^2+(0-1)^2}\) = \(\sqrt{(0-5)^2+(y-5)^2+(0-2)^2}\)
Squaring both sides,
(0 - 3)2 + (y - 1)2 + (0 - 1)2 = (0 - 5)2 + (y - 5)2 + (0 - 2)2
9 + y2 - 2y +1 + 4 = 25 + y2 -10y + 25 + 4
8y = 40
Y = 5
The point C is (0,5,0).