By memorizing the standard form of a circle, knowing
how to compare a given standard form to it, and
how to pick out the center and the radius:

Rule:
The standard form of a circle is

(x - h)² + (y - k)² = r²

with center (h,k) and radius r.

So compare your equation:

(x - 4)² + (y + 8)² = 9  to

(x - h)² + (y - k)² = r²

and you can see that

-h = -4 or h = 4,
-k = +8 or k = -8,
 r² = 9 so r = 3

So the center is (h,k) = (4,-8) and the radius is r = 3.

-------------------------------------------

You don't need to check it, but let's do it anyway,
so you'll know why it's true and learn something
about the equation of a circle:

Draw the circle with center (4,-8) and radius = 3

 

The left-most point of the circle should be 3 units left
of the center or (1,-8). 



Let's see if that satisfies the
equation 

(x - 4)² + (y + 8)² = 9
(1 - 4)² + (-8 + 8) = 9
         (-3)² + 0² = 9
              9 + 0 = 9
                  9 = 9

Yes it does.
 
The upper-most point of the circle should be 3 units above
the center or (4,-5).  



Let's see if that satisfies the
equation 

(x - 4)² + (y + 8)² = 9
(4 - 4)² + (-5 + 8) = 9
       (0)² + (-3)² = 9
              0 + 9 = 9
                  9 = 9

Yes it does.

The right-most point of the circle should be 3 units right
of the center or (7,-8).  



Let's see if that satisfies the
equation 

(x - 4)² + (y + 8)² = 9
(7 - 4)² + (-8 + 8) = 9
          (3)² + 0² = 9
              9 + 0 = 9
                  9 = 9

Yes it does.

The lowest point of the circle should be 3 units below
of the center or (4,-11).  



Let's see if that satisfies the
equation 

 (x - 4)² + (y + 8)² = 9
(4 - 4)² + (-11 + 8) = 9
        (0)² + (-3)² = 9
              0 + 9 = 9
                  9 = 9

Yes it does.  So we know the center is (4,-8) and the radius 
is 3.

Edwin