math help plz!!!

[RING12]

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find the center and the radius of the circle X^2+y^2+6y+8=0


the answer is r=1 and center is (0,3). I cant figure it out how, can some one explain this to me please!!!!!

 

[mh0000]

look up "completing the square." This will get it into a form of (x-h)^2+(y-k)^2 = r^2. Once in this form, you will see that the center point is (h,k) and the radius is the sqrt of r^2.

 

[rockclock]

find the center and the radius of the circle X^2+y^2+6y+8=0


the answer is r=1 and center is (0,3). I cant figure it out how, can some one explain this to me please!!!!!

completing the square is basically this:

(x+a/2)^2 = x^2 + ax + a^2/4

so if you have x^2 + ax, you know that you have to add a^2/4 to both sides to be able to get it into (x+__)^2 form. in this problem, there is no ax term so you're already good on x's. there is a 6y that you will need to collapse into (y+__)^2 form.

x^2 + y^2 + 6y + 8 = 0

x^2 + y^2 + 6y + 9 + 8 = 9

(x-0)^2 + (y+3)^2 + 8 = 9

(x-0)^2 + (y+3)^2 = 1

that's a circle centered at x=0, y=-3, with radius 1.