Find the center and radius of the circle

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$\text{Find the center and radius of the circle given by the equation: }x^{2}+y^{2}+12y+35 = 0 $

**Answer**

$x^{2}+y^{2}+12y+35 = 0 $

$x^2+y^2+12y=-35$

$x^2+y^2+12y+36=-35+36$

$\left(x\right)^2+\left(y+6\right)^2 = 1$

$\left(x\right)^2+\left(y+6\right)^2 = {\left(1\right)}^{2}$

$\text{The center of the circle is }\left(0,-6\right)\text{ and radius = }1$