Hello!
First, let's write some important information:
Center = (0, 0), r = 4.
To write the equation of the circle, we must use the formula below:
[tex]\left(x-x_C\right)^2+(y-y_C)^2=r^2[/tex]As we know the values of the center and the radius, let's replace them in the equation:
[tex]\begin{gathered} \left(x-0\right)^2+(y-0)^2=4^2 \\ \\ \boxed{x^2+y^2=16} \end{gathered}[/tex]Alternative C.
