Question

how to find when a circle is centered on the x-axis ?

Answer 1

The x-intercepts are the x-coordinates of the points where the graph crosses the x-axis. Thus, for these points the y-coordinate is zero. Thus, in the equation set y = 0 and solve for x. Similarly to find the y-intercepts, set x = 0 in the equation and solve for x.

Hope that helped! :)

Answer 2

in form
$(x-h)^2+(y-k)^2=r^2$
the circle has a center of (h,k) and radius of r

when a circle is on the x axis, y=0
so when k=0

so if you have anything like this
$(x-h)^2+(y-0)^2=r^2$ or more simply
$(x-h)^2+y^2=r^2$