3rd condition to determine a Circle

Question

Find the equation of a circle touching the x-axis and passing through the points (7, -2) and (0, -9)
Ans:
x^2 + y^2 - 30x + 34y + 225=0 and
x^2 + y^2 - 6x + 10y + 9=0

need a solution for these :) thanks

Answer 1

circle passing through (7,-2) and (0,-9)

(x-h)^2 + (y-k)^2 = r^2

(7-h)^2 + (-2-k)^2 = r^2

49-14h + h^2 + 4 -4k +k^2 = r^2

h^2 + 81 -18k +k^2 = r^2

49-4h -77 +18k = 0

4h-18k = -28

2h -9k =-14

h = 4.5k - 7

1st given answer has 15 and -17 for h and k

15 doesn't = 4.5(-17)-7

2nd given answer has 3 and -5 for h and k

3 doesn't equal 4.5(-5)-7

neither answer is correct