F5 math problems ( Equation of Circles )

Since the circle touches the x-axis at (3, 0), the centre of it has x-coordinate = 3 and therefore can be expressed as (3, k) where k is some value to be found.
Then, radius of the circle is also k and the distance between (0, 5) and (3, k) is also k, i.e.
√[(3 - 0)2 + (k - 5)2] = k
9 + k2 - 10k + 25 = k2
10k = 34
k = 17/5
Hence, the equation of the circle is:
(x - 3)2 + (y - 17/5)2 = (17/5)2
x2 - 6x + 9 + y2 - 34y/5 = 0
x2 + y2 - 6x - 34y/5 + 9 = 0