Answer: To determine the center and radius of the circle given by the equation:
(x - 1)^2 + (y - 9)^2 = 36.
We can identify the center and radius using the standard form of the circle equation:
(x - h)^2 + (y - k)^2 = r^2,
where (h, k) represents the center of the circle, and r is the radius.
Comparing the given equation with the standard form, we can see that:
h = 1 (the x-coordinate of the center),
k = 9 (the y-coordinate of the center),
r^2 = 36 (from the right-hand side of the equation).
To find the radius (r), we simply take the square root of r^2:
r = √36 = 6.
So, the center of the circle is (1, 9), and the radius is 6 units.