SOLUTION: What is the graph of the equation x2 + y2 - 8x + 6y + 24 = 0

We must first get the equation in standard form:

 

Rearrange to get the x terms together and the y terms togethsr.
That is, swap the middle two terms:






Out to the side or on scratch paper,

we complete the square of

:

1. Multiply the coefficient, -8, of , by ,
   getting .
2. Then square , getting +16
3. Add +16 to the left side inside the first parentheses, and
   also add it to the right side:

   

Now we complete the square of

:

1. Multiply the coefficient, 6, of , by ,
   getting .
2. Then square , getting +9
3. Add +9 to the left side inside the first parentheses, and
   also add it to the right side:

 

Factor each parentheses:



Write as perfect squares:



Add -24 to both sides:



Compare to the standard form:



This has center (h,k) and radius r.

 so , , so .  , so 

so the center, (h,k) = (4,-3) and the radius is 1.

So we plot the center (4,-3).



Get a compass and open it one unit wide.  Place the sharp 
point of the compass on the center and draw the circle.
That is the graph:



Edwin