we know that
the standard form equation of the circle is
(x-h)²+(y-k)²=r²
where
(h,k)------> is the center
and
r----> is the radius
let
A------> the point (−8, 0)
B-------> the point (−12, 2)
step 1
find the distance point A and point B
d=√[(2-0)²+(-12+8)²]------> d=√20-----> d=2√5 units
the distance AB is equals to the diameter
and
the radius r=2√5/2-----> r=√5 units
step 2 find the midpoint AB
midpoint ABx=(-8-12)/2-----> -10
midpoint ABy=(2+0)/2-----> 1
the midpoint is (-10,1)
the center is equal to the midpoint
so
(h,k)------> (-10,1)
step 3
find the equation of a circle
(x-h)²+(y-k)²=r²------> (x+10)²+(y-1)²=(√5)²
(x+10)²+(y-1)²=5
the answer is
(x+10)²+(y-1)²=5
see the attached figure
