Which of the following circles have their centers on the x-axis?Check all that apply.

To determine which circles have their centers on the x-axis, we need to analyze the general equation of a circle, which is given by:

$(x - h)^2 + (y - k)^2 = r^2$

In this equation:

• $(h, k)$ represents the center of the circle.
• $r$ is the radius.

For a circle to have its center on the x-axis, the $y$-coordinate of the center $k$ must be zero. Therefore, we are looking for circles where the center is of the form $(h, 0)$.

Steps to Check Each Circle:

1. Check the center of each circle given in the options.
2. Identify if the $y$-coordinate of the center is 0.

Final Answer

The circles that have their centers on the x-axis are those that show a center of the form $(h, 0)$, where $h$ can be any real number. Check the options you have for those that meet this condition.