Question 967614
Start this way:


Understand through intuition, the center of the circle is on the x-axis. and this is some unknown point (x,0).


Distance from (x,0) Center to A(1,2) is equal to distance from (x,0) center to B(1,-2).  Setup this using the distance formula and find the x value for the center point of the circle.


Now, can you think a way to use the given line touching the circle?
Equivalent line is{{{ y=-x/2-5/2}}} and is some general point  (x, -(x/2+5/2) );


Unfinished; just a description to begin solving.