Since we have the endpoints of a diameter the center is very easy to find. It is the midpoint of the diameter endpoints, which is just the average coordinates...
The center is:
((-7+3)/2, (-10+2)/2)
(-2,-4)
To find the radius we can use the endpoints again to find the diameter squared and then get the radius from that:
d^2=(dy)^2+(dx)^2
d^2=(2--10)^2+(3--7)^2
d^2=12^2+10^2
d^2=144+100
d^2=244
d=√244, since d=2r, r=d/2
r=√(244/4)
r=√61
The equation of a circle is (x-h)^2+(y-k)^2=r^2. We found earlier that the center was at (-2,-4) and we just saw that r^2=61 so:
(x+2)^2+(y+4)^2=61
