Which of the following circles lie completely within the fourth quadrant?

Check all that apply.

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

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

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

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

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