You should have a standard strucutre for a circle.
(x-h)^2 + (y-k)^2 = r^2
(h,k) is the center of the circle.
r is the radius of the circle
In this case, you are given the center, (1,7).
This gives (x-1)^2 + (y-7)^2 = r^2
You are given a hint to find the radius. If the circle is tangent to the y-axis, there is only one way to do that. The point (0,7) must lie on the circle. This makes the radius 1.
This gives (x-1)^2 + (y-7)^2 = 1^2
Note: It is important that it is TANGENT to the y-axis. If it said only that it intersected the y-axis, there would be possibly two points of intersection. With a tangent, there is only one such point.