Answer:
[tex]x^{2} +y^{2} =36[/tex]
Step-by-step explanation:
A circle centered at (0,0) with radius r is [tex]x^{2} +y^{2} =r^{2}[/tex]
Since your circle has diameter of 12, then its radius is 6. Then [tex]r^{2} =36[/tex]
So a possible answer is: [tex]x^{2} +y^{2} =36[/tex]
If you want to move the location of the center, but keep it on the x-axis, then add or subtract a number to the x, such as this:
[tex](x+4)^{2} +y^{2} =36[/tex]
The center of this circle would be (-4, 0) which is still on the x-axis.
