Write the equation of the circle centered at $(-8,8)$ with diameter 14 .

Step 1 ：The equation of a circle is given by \((x-a)^2 + (y-b)^2 = r^2\), where \((a,b)\) is the center of the circle and \(r\) is the radius.

Step 2 ：In this case, the center of the circle is given as \((-8,8)\) and the diameter is 14, so the radius is half of the diameter, which is 7.

Step 3 ：We can substitute these values into the equation to get the equation of the circle.

Step 4 ：The equation of the circle is \((x - (-8))^2 + (y - (8))^2 = 7.0^2\).

Step 5 ：Final Answer: The equation of the circle is \(\boxed{(x - (-8))^2 + (y - (8))^2 = 7.0^2}\).