Which of the following circles lie completely within the fourth quadrant?Check all that apply.A.(x - 5)2 + (y + 5)2 = 9B.(x - 9)2 + (y + 9)2 = 16C.(x - 12)2 + (y + 0)2 = 72D.(x - 2)2 + (y + 7)2 = 64

The equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

The fourth quadrant is where x > 0 and y < 0.

Let's check each circle:

A. (x - 5)² + (y + 5)² = 9 The center is at (5, -5) and the radius is √9 = 3. The circle extends 3 units in all directions from the center, so it extends to x = 5 - 3 = 2 and y = -5 - 3 = -8. Both of these are in the fourth quadrant, so circle A is completely within the fourth quadrant.

B. (x - 9)² + (y + 9)² = 16 The center is at (9, -9) and the radius is √16 = 4. The circle extends to x = 9 - 4 = 5 and y = -9 - 4 = -13. Both of these are in the fourth quadrant, so circle B is completely within the fourth quadrant.

C. (x - 12)² + (y + 0)² = 72 The center is at (12, 0) and the radius is √72 = 8.48 (approximately). The circle extends to x = 12 - 8.48 = 3.52 and y = 0 - 8.48 = -8.48. The x-coordinate is in the fourth quadrant, but the y-coordinate is not, so circle C is not completely within the fourth quadrant.

D. (x - 2)² + (y + 7)² = 64 The center is at (2, -7) and the radius is √64 = 8. The circle extends to x = 2 - 8 = -6 and y = -7 - 8 = -15. The x-coordinate is not in the fourth quadrant, so circle D is not completely within the fourth quadrant.

So, the circles that lie completely within the fourth quadrant are A and B.