Question 65752
let the  point on the Y axsi be (0,y)which  is equidistance from P(0,8) and Q(-4,4) 
 applying distance formula we get sqrt[(8-y)^2]=sqrt[(4)^2 +(4-y)^2]
       or   8-y = sqrt[ 16 + 16 +y^2 -8y]
       or (8-y)^2=32 + y^2 -8y
       or  64 - 16y + y^2 =32 + y^2 -8y
       or   32=8y
        y=4

required point is (0,4)