hello :
let two points : A (a,b) , B (a' , b')
the center of the circle of diameter : [AB] is (X0 , Y0) :
X0 = (a+b)/2 and Y0 = (a'+b')/2
the ridus is : r = AB/2
AB = √((a'-a)²+(b'-b)²)
the standard form of the equation of the circle is :
(x-X0)² + (y -Y0)² = (AB/2)²