SOLUTION: x^2+y^2=6y sketch the graph of the equation. This is one of the questions that are difficult for me

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Question 103632: x^2+y^2=6y sketch the graph of the equation. This is one of the questions that are difficult for me
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+y^2=6y
Best bet is to complete the square for y and see where we are then.
x%5E2%2By%5E2-6y=6y-6y
x%5E2%2By%5E2-6y=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%5E2%2By%5E2-6y%2B9=9
x%5E2%2B%28y-3%29%5E2=9
OK. If you compare this equation with the equation of a circle of radius, R, centered at (h,k):
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
You get
x-h=x
h=0
y-k=y-3
k=3
R%5E2=9
R=3
Your equation is a circle centered at (0,3) with a radius of 3.