Question 809841
You are mainly looking for points A and B, for which y=0.


Checking about the circle, {{{(x-4)^2+(y+2)^2=r^2}}}.
You use distance formula to find r, which is distance from C to O.  This is easy to see on a graph, since the two points are on the vertical line x=4.  The radius is (2)+|-2|=4.  No need for the distance formula in this case.  Then the circle's equation is {{{(x-4)^2+(y+2)^2=4^2 }}}.


Does a graph give you some idea how to complete answering the question?


{{{graph(300,300,-9,9,-9,9,-2+sqrt(16-(x-4)^2),-2-sqrt(16-(x-4)^2))}}}