If the circle is tangent to the y axis at (0,2) the center must be (c , 2) where c is the radius
Using the squares of the distance formula
(c- 0)^2 + ( 2 - 2)^2 = (12 - c)^2 + (2 - 0)^2
c^2 = c^2 - 24c + 144 + 4
24c = 148
c = 148/24 = 37/6 = the radius
