The curve is given to be:
[tex]x^2+y^2+12y=0[/tex]
We can rewrite the equation in the form:
[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]
Using the Completing the Square method, we have the equation to be:
[tex]\frac{\left(x-0\right)^2}{6^2}+\frac{\left(y-\left(-6\right)\right)^2}{6^2}=1[/tex]
Therefore, the ellipse's center is (0, -6).
