Question:
Find the point on the y-axis which is equidistant from the points A(3, 1, 2) and B(5, 5, 2).
Solution:
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
$\sqrt{(0-3)^{2}+(y-1)^{2}+(0-2)^{2}}=\sqrt{(0-5)^{2}+(y-5)^{2}+(0-2)^{2}}$
Squaring both sides,
$(0-3)^{2}+(y-1)^{2}+(0-2)^{2}=(0-5)^{2}+(y-5)^{2}+(0-2)^{2}$
$9+y^{2}-2 y+1+4=25+y^{2}-10 y+25+4$
8y = 40
Y = 5
The point C is (0,5,0).