first, find the midpoint of the diameter. the midpoint is the center of the circle.
[(-10+(-6)]/2=-8, [(-8+(-2)]/2=-5
so the center is at (-8, -5)
next, find the distance between the two points:
d=√[-6-(-10)]²+[-2-(-8)]²=√4²+6²=√52=2√13
half of the diameter is radius, r=half of 2√13=√13
standard equation for the circle is (x-h)²+(y-k)²=r², (h,k) being the center, r the radius
(x+8)²+(y+5)²=13 is the answer.
