The equation of a circle is given by:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where (a,b) = coordinate of the extermal point} \\ r\text{ = radius of the circle} \end{gathered}[/tex]From the question given,
a = -1
b = 4
r = 4
If we substitute these values into the equation of the circle
[tex](x-(-1))^2+\text{ (y -4)}^2=4^2[/tex][tex](x+1)^2+(y-4)^2\text{ = }16[/tex]Option D is correct
