To write the equation of a circle centered at (h, k) with a diameter of d, we can use the standard form of the equation:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the center of the circle and r represents the radius.
In this case, the center of the circle is (-4, 4), and the diameter is 14. The radius is half of the diameter, so the radius would be 14 / 2 = 7.
Substituting the values into the equation, we have:
(x - (-4))^2 + (y - 4)^2 = 7^2
Simplifying further:
(x + 4)^2 + (y - 4)^2 = 49
Therefore, the equation of the circle centered at (-4, 4) with a diameter of 14 is:
(x + 4)^2 + (y - 4)^2 = 49