In the standard equation for a circle centered at any point a change in the value of the number that is part of the xterm results in a vertical movement?

In the standard equation of a circle, ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) is the center and (r) is the radius, a change in the value of (h) (the x-coordinate of the center) results in a horizontal movement of the circle along the x-axis, not a vertical movement. Vertical movement is instead influenced by changes in (k), the y-coordinate of the center. Thus, altering the x-term affects the circle's left-right position, while changes to the y-term affect its up-down position.