Hi!
It is known that the equation for any circle is given as:
(x-h)2+(y-k)2 = r2
where (h,k) is the center, and r is the radius. We're gonna need these three pieces for any equation of a circle!
Let's start with h and k. Since we know how long our circle is (that's the diameter), to find the center, we can cut it in half using the best "cut-in-half" points formula there is - the midpoint formula. This is given as
(x1+x2)/2 + (y1+y2)/2 . Plugging in the points for our diameter, we get...
Center: (h,k) = (2,-5).
Lastly, to find how long the r actually is, we need to know the distance from the radius to the outside of the circle! For this, we have the two points we need, so let's use the distance formula. I will plug in my newfound center, as well as choose an endpoint - I'll choose (-2,-8) since it will get subracted anyways. We now have:
Sqrt ((y1-y2)2+(x1-x2)2)
Substitute your center and the diameter point. (order for x and y actually doesn't matter, just as long as you make sure signs are correct!)
Sqrt ((-5+8)2+(2+2)2)= Sqrt (9+16) = Sqrt (25) = 5.
Thus, r = 5.
These are the three pieces you need for any equation of a circle. Just plug those in and I think you can take it from there!
