Answer
$x^2+(y+4\sqrt 3)^2=64$
Work Step by Step
$(x-h)^2=4p(y-k)$
or, $(4-0)^2=4p(0-4)$
or, $p=-1$
Now, $x^2=-4(y-4)$
The x-coordinate of the center of the circle is: $4^2 +y^2 =8^2$
or, $y=-\sqrt {8^2-4^2}=-4\sqrt 3$
The equation of a circle is: $(x-h)^2+(y-k)^2=r^2$
or, $x^2+(y+4\sqrt 3)^2=64$
