Question

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

Answer 1

C and D

Explanation:

The fourth quadrant is the bottom, right quadrant. In the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative.

For a circle to be completely within the fourth quadrant, the circle must have its center in the fourth quadrant, and the center has to be far away enough from the positive x-axis and from the negative y-axis, that no points on the circle are outside the fourth quadrant.

Choice A has center (12, 0), so it cannot be.

Choice B has center (2, -7) and radius 8. Many points will be past the axes.

Choice C has center (9, -9) and radius 4. All points will be in the fourth quadrant.

Choice D has center (9, -5) and radius 3. All points will be in the fourth quadrant.

Answer 2

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

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

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