Respuesta :

The general equation of a circle is

[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ Where} \\ (h,k)\text{ are the coordinates of the center and} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]

So, in this case, you have

[tex]\begin{gathered} (h,k)=(0,5) \\ \text{ Then} \\ h=0 \\ k=5 \\ \text{ and} \\ r=8 \end{gathered}[/tex]

Then,

[tex](x-0)^2+(y-5)^2=8^2[/tex]

Therefore, the equation of the circle is

[tex]x^2+\mleft(y-5\mright)^2=64[/tex]