1. Circle Graph

What would this graph look like: $3y^2 + 3x^2 + 12y=0$.

I know that it is a circle but how do I work out the center and the radius of it? Thanks in advance.

2. Originally Posted by Air
What would this graph look like: $3y^2 + 3x^2 + 12y=0$.

I know that it is a circle but how do I work out the center and the radius of it? Thanks in advance.
divide through by 3 and group the y's. you will get:

$x^2 + (y^2 + 4y) = 0$

now complete the square for the y's and get your equation in the form: $(x - h)^2 + (y - k)^2 = r^2$ (we already know h = 0)

the center is (h,k) and the radius is r

3. Originally Posted by Air
What would this graph look like: $3y^2 + 3x^2 + 12y=0$.

I know that it is a circle but how do I work out the center and the radius of it? Thanks in advance.
You should not have been given this problem without a refresher on "Completing the Square". complete the Square on the 'y's and you will be done.

$3x^2 + 3y^2 + 12y = 0$

$x^2 + y^2 + 4y = 0$

$x^2 + (y^2 + 4y + something) = something$

$4/2 = 2$
$2^2 = 4 = something$

$x^2 + (y^2 + 4y + 4) = 4$

I'll leave you the last step.