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}+16y+39 = 0 $

**Answer**

$x^{2}+y^{2}+16y+39 = 0 $

$x^2+y^2+16y=-39$

$x^2+y^2+16y+64=-39+64$

$\left(x\right)^2+\left(y+8\right)^2 = 25$

$\left(x\right)^2+\left(y+8\right)^2 = {\left(5\right)}^{2}$

$\text{The center of the circle is }\left(0,-8\right)\text{ and radius = }5$