I have a question about the following problem and the two points need not be located on the circumference of such smallest circle. I know this is a linear-programming problem but I just don't know how to solve it mathematically.Give two planar points p1=(a1,b1) and p2=(a2,b2) and a line y=0,   design an algorithm to find the smallest circle that covers  both points such that its center (x*, 0) lies on y=0.
smallest circle that covers two points with its center in x axis
algorithms;optimization;computational geometry