Question 714404
The tangent lines touch the circle at the top and the bottom. 
This means that the diameter of the circle is the distance between the two tangent lines 6-1=5.
So r = 2.5, and the center of the circle lies halfway in between y=1 and y=6.
So the center has the coordinates (a,3.5) and the radius is 2.5:
(x-a)^2 + (y-3.5)^2 = 2.5^2
We can use the point (2,2) on the circle to find a:
(2-a)^2 + (2-3.5)^2 = 2.5^2
This simplifies to a^2 - 4a = 0
a(a-4) = 0
There are two possibilities, a=0 and a=4.
So there are two circles which fit the criteria:
x^2 + (y-3.5)^2 = 6.25
(x-4)^2 + (y-3.5)^2 = 6.25