For question one:
Let the center of the circle be (h, k).
Since the circle is tangent to the y-axis, the point (0, k) is on the circle.
And since both (2,0) and (8,0) are on the circle, they form an isosceles triangle with (h, k), which means that h = 5. Hence, (h, k) = (5, k). So the radius of the circle is 5.
Solving for k by using the distance formula:
Hence the two equations are: