**Answer:**

C. (X-9)^9 + (y+9)^2= 16

D. (X-9)^2 + (y+5)^2= 9

**Step-by-step explanation:**

The formula for a circle is

(X-h)^2 + (y-k)^2= r^2

where (h,k) is the center of the circle and r is the radius

The 4th quadrant is where x is positive and y is negative

Add r to the y coordinate of the center and if it is still negative, the circle is still completely in the 4th quadrant

A. (X-12)^2 + (y+0)^2= 72

The center is at 12,0 and the radius is sqrt(72) = 6sqrt(2)

This will be positive so it goes into the 1st quadrant

B. (X-2)^2 + (y+7)^2= 64

The center is at 2,-7 and the radius is 8

-7+8=1 so it goes into the 1st quadrant

C. (X-9)^9 + (y+9)^2= 16

The center is at 9,-9 and the radius is 4

-9+4 = -5 so it is completely in the 4th quadrant

D. (X-9)^2 + (y+5)^2= 9

The center is at 9,-5 and the radius is 3

-5+3 = -2 so it is completely in the 4th quadrant