Write an equation for a circle with a diameter of that has endpoints at (8,7) and (-4,-3). round to the nearest tenth if necessary.

 Using the distance formula,
d = sqrt(x2-x1)^2 +(y2-y1)^2 .
Substituting the values of x and y.
we get,
d = sqrt(-4-8)^2 +(-3-7)^2
d = 2 sqrt 61 

diameter = 2*radius
               = 2 sqrt 61
               = 2 r
               = r
               = sqrt 61
           r^2 = 61 

midpoint of the diameter is: 

Xm= 8-4 / 2
      = 2 
Ym = 7-3 / 2 
      = 2 
Hence,
The center is (2,2) 

General equation of a circle is:
(x-x1)² +(y-y1)² =r²
with,
(x1,y1) being the center of the circle. 
Substituting the values:

(x-2)+(y-2) = 61