Question

question 9 of 10 which of the following circles have their centers on the x - axis? check all that apply. a. (x - 4)^2+(y - 0)^2 = 22 b. (x - 0)^2+(y - 0)^2 = 25 c. (x + 1)^2+(y - 7)^2 = 16 d. (x - 0)^2+(y - 5)^2 = 49

Explanation:

Step1: Recall circle - center formula

The standard form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle.

Step2: Analyze option A

For the circle $(x - 4)^2+(y - 0)^2=22$, the center is $(4,0)$. Since the $y$ - coordinate of the center is $0$, the center lies on the $x$ - axis.

Step3: Analyze option B

For the circle $(x - 0)^2+(y - 0)^2=25$, the center is $(0,0)$. Since the $y$ - coordinate of the center is $0$, the center lies on the $x$ - axis.

Step4: Analyze option C

For the circle $(x + 1)^2+(y - 7)^2=16$, the center is $(-1,7)$. Since the $y$ - coordinate of the center is $7
eq0$, the center does not lie on the $x$ - axis.

Step5: Analyze option D

For the circle $(x - 0)^2+(y - 5)^2=49$, the center is $(0,5)$. Since the $y$ - coordinate of the center is $5
eq0$, the center does not lie on the $x$ - axis.

Answer:

A. $(x - 4)^2+(y - 0)^2=22$
B. $(x - 0)^2+(y - 0)^2=25$