Question

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

A. (x-4)²+(y-0)²=74
B. (x-2)²+(y+3)²=2
C. (x-0)²+(y-0)²=7²
D. (x-0)²+(y-3)²=23

Answer 1

To identify the circles with their centers on the x-axis, we need to examine the equations and determine the coordinates of their centers.

Step-by-step explanation:

To determine which circles have their centers on the x-axis, we need to examine the equations and identify those that have a y-coordinate of 0 for their center.

A. The equation (x-4)²+(y-0)²=74 has a center at (4, 0), so it has its center on the x-axis.

B. The equation (x-2)²+(y+3)²=2 has a center at (2, -3), which is not on the x-axis.

C. The equation (x-0)²+(y-0)²=7² has a center at (0, 0), so it has its center on the x-axis.

D. The equation (x-0)²+(y-3)²=23 has a center at (0, 3), which is not on the x-axis.

Therefore, the circles with their centers on the x-axis are A and C.