The equation of a circle with center (h, k) and radius r is given by:
\[(x-h)^2 + (y-k)^2 = r^2\]
In this case, the circle passes through (2, 2) and is centered at (5, 6). To find the radius, we can use the distance formula between the center of the circle and the point it passes through:
\[r = \sqrt{(5-2)^2 + (6-2)^2}\]
\[r = \sqrt{3^2 + 4^2}\]
\[r = \sqrt{9 + 16}\]
\[r = \sqrt{25}\]
\[r = 5\]
Therefore, the equation of the circle is:
\[(x-5)^2 + (y-6)^2 = 5^2\]
\[(x-5)^2 + (y-6)^2 = 25\]
So, the correct answer is D. \[(x-5)^2 + (y-6)^2 = 25\].
