This is the equation of a circle because it has 
both an  and a  term which have
the same coefficients when on the same side of the
equation.

We want to get it looking like this standard form
for a circle's equation:



where the center is (h,k) and the radius is r



Divide through by 3



Swap the two middle terms to get the x-term next to
the -term and the -term next to the
y-term. Also add 4 to both sides:



Complete the square on the first two terms:

1. Multiply the coefficient of x, which is -4, by 
   getting -2
2. Square -2, getting  or .
3. Add  to both sides:



Complete the square on the last two terms on the left:

1. Multiply the coefficient of y, which is -8, by 
   getting -4
2. Square -4, getting  or .
3. Add  to both sides:



1. Factor the trinomial consisting of the first three terms on the left.
2. Factor the trinomial consisting of the last three terms on the left.
3. Combine the numbers on the right.



Write the  as 

Compare to



and the center is (h,k) = (2,4) and the radius is r=4

The graph is drawn with a compass, since it is a circle.

Put the sharp point of the compass at the center (2,3):



 Open the compass to 4 units, and draw this circle:



Edwin