(x^2+6x+9) + (y^2-4y+4)= 12+9+4 is equal to (x+3)^2 + (y-2)^2=25
How, if this works, is it related to a perfect square quadratic? Have we seen this work done before with something other than circles?
This question was asked before. The answer can be found here:
http://www.jiskha.com/display.cgi?id=1259177765
Yes, what your teacher was (probably) trying to do is to transform the equation of a circle to its standard form.
This standard form is:
(x-x1)²+(y-y1)² = r²
Therefore, by comparison with the standard form of the circle, x=-3, y=2 and r=5, which represents a circle of radius 5, whose centre is at the point (-3,2).