Ok, this is kinda crazy, but I THINK I got it. If the circle is tangent to the point (1,0), that means that if the radius is a length of 5, from the y coordinate of 0, you are going up 5 units to meet the center of the circle. That puts the vertex at that x coordinate which is 1, and the y coordinate which is 5. So using that info, the equation for the circle is (x-1)^2 + (y-5)^2 = 25. Now to find the y intercepts, we set x equal to 0: (0-1)^2 + (y-5)^2 = 25. -1 squared is 1. Subtract that from both sides to get (y-5)^2 = 24. Now, undo that square by taking the square root of both sides (using your calculator) to get
y-5= +/-4.89898. Now add 5 to both sides to get y values of 9.89898 and .10102