Question 103632
x^2+y^2=6y
Best bet is to complete the square for y and see where we are then.
{{{x^2+y^2-6y=6y-6y}}}
{{{x^2+y^2-6y=0}}}
Completing the square for y:
(y+A)^2=y^2+2A+A^2
If I compare terms in your equation and this equation, I see that:
2Ay=-6y
2A=-6
A=-3
Once I know A, then 
A^2 = 9
If I add 9 to both sides of the equation, I get:0
{{{x^2+y^2-6y+9=9}}}
{{{x^2+(y-3)^2=9}}}
OK. If you compare this equation with the equation of a circle of radius, R, centered at (h,k):
{{{(x-h)^2+(y-k)^2=R^2}}}
You get
{{{x-h=x}}}
{{{h=0}}}
{{{y-k=y-3}}}
{{{k=3}}}
{{{R^2=9}}}
{{{R=3}}}
Your equation is a circle centered at (0,3) with a radius of 3. 
{{{drawing( 300, 300, -4, 7, -4, 7,grid( 1 ),circle( 0, 3, .2 ),green(circle(0,3,3)))}}}