General 2nd degree equation needing factoring, fractions: Find the center and radius of a circle determined by
We need to rewrite this in the form of the standard equation of a circle. Once we do, we can read the coordinates (h,k) of the center and the value of the radius. Since the coefficients of the square terms must be one, we divide by 9 to get
We need to complete the squares by determining what constant terms could be added make the forms (x - h)2 and (y - k)2. First we move the constant to the right hand side and group the other terms:
We see that if we add 
to the first group, we would have the square of 
, and if we add 
to the second group we would have the square of 
. Of course we need to add similar amounts to the right hand side to compensate. Here are the details:
, or
Comparing this with the standard equation of a circle, we see that the center is at 
and the radius is 
.