If the endpoints of the diameter of a circle are (6, 3) and (2, 1), what is the standard form equation of the circle?

If the endpoints of a diameter are (6,3) and (2,1) the midpoint is the center of the circle so:

(x,y)=((6+2)/2, (3+1)/2)=(4,2)

Now we need to find the radiusthe diameter is:

d^2=(6-2)^2+(3-1)^2

d^2=16+4

d^2=20  since d=2r, r=d/2, and r^2=d^2/4 so

r^2=5

The standard form of the circle is (x-h)^2+(y-k)^2=r^2 and we know:
 
(h,k)=(4,2) from earlier so:

(x-4)^2+(y-2)^2=5