So if your center is on the y axis it means the x coordinate is 0 and since the distance from center of circle to the points it contains is equal, if (0, y) was our center.

Distance between (0,y) and (1,4) = Distance between (0,y) and (-3,2)

So using the distance formula. Distance between (0,y) and (1,4) =

Distane between (0,y) and (-3,2) is

so or

which gives the identity, or y = 1

so (0,1) is your center and is your radius.