What is the graph of the equation x2 + y2 - 8x + 6y + 24 = 0
This is a circle because
and
have the
same coefficient when on the same side of the equation.

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