Find the coordinates of point on `Y`-axis which is equidistant from points `(13, 2)` and `(12,-3)` .

Explanation

Let P(0, y) be the required point and the given points be A (12 , -3) and B (13, 2).
Then PA = PB (given)

`sqrt((12-0)^(2) + (-3 -y)^(2)) = sqrt((13-0)^(2) + (2-y)^(2))`
`implies sqrt(144 + (y + 3)^(2)) = sqrt(169 + (2-y)^(2))`
Taking squares on both sides , we get
`169 + 4 + y^(2) - 4y = 144 + 9 + y^(2) + 6y`
`implies 10y = 20 implies y = 2`
`therefore` The required point on Y-axis is (0,2).