Step-by-step explanation:
Given equation of circle is:
[tex] {x}^{2} + (y + 4)^{2} = 64 \\ {(x - 0)}^{2} + {(y + 4)}^{2} = {8}^{2} \\ equating \: it \: with \\ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ we \: find: \\ - h = 0 \implies \: h = 0 \\ - k = 4\implies \: k= - 4 \\ \therefore \: center = (h \: k) \\ \red{ \boxed{\bold {\therefore \: center = (0 \: - 4)}}} \\ \\ \: \: \: \purple{ \boxed{\bold {radius \: r = 8 \: units}}}[/tex]
