Consider, C(x,y,z) point equidistant from points A(-1, 2, 3) and B(3, 2, 1).
∴ AC = BC
\(\sqrt{(x+1)^2+(y-2)^2+(z-3)^2}\) = \(\sqrt{(x-3)^2+(y-2)^2+(z-1)^2}\)
Squaring both sides,
(x + 1)2 +(y - 2)2 + (z - 3)2 = (x - 3)2 + (y - 2)2 + (z - 1)2
x2 + 2x + 1 + y2 - 4y + 4 + z2 - 6z + 9 = x2 - 6x + 9 + y2 - 4y + 4 + z2 - 2z +1
8x - 4z = 0
Equation of curve is 8x - 4z = 0