To write the standard form of the equation of a circle, we use the formula:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Where:
- \( (h, k) \) are the coordinates of the center of the circle.
- \( r \) is the radius of the circle.
Given that the center of the circle is \( (9, -9) \), we can identify \( h = 9 \) and \( k = -9 \). And since the radius of the circle is given as \( r = 12 \), we can substitute these values directly into the formula:
\[
(x - 9)^2 + (y - (-9))^2 = 12^2
\]
Simplifying further by squaring the radius:
\[
(x - 9)^2 + (y + 9)^2 = 144
\]
This equation is the standard form for the circle with center at \( (9, -9) \) and radius 12.
