Find the equation of the circle which is tangent to the x-axis at (2,0) and touches the line y=6.

Centre (2,3) radius3

(X-2)^2+(y-3)^2=9

If it's tangent to the x axis at (2,0)  and touches the line y = 6, the diameter must be 6, so the radius must be 3

And, it must touch the line y = 6 at the point (2,6)

Then, the midpoint of (2,0) and (2,6)  must be the center -1/2 of the diameter -, so we have  the center as :

 ([ 2 + 2] /2 , [6 + 0]/2 )   = (4/2 , 6/2 ) =  ( 2, 3)

So....the equation of the circle is    (x - 2)^2 + (y -3)^2  = 9

Here's a graph :   https://www.desmos.com/calculator/z4nkt0mtbr