Question

A circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle?

Answer 1

Answer:

$x^{2} +y^{2} =36$

Step-by-step explanation:

A circle centered at (0,0) with radius r is $x^{2} +y^{2} =r^{2}$

Since your circle has diameter of 12, then its radius is 6.  Then $r^{2} =36$

So a possible answer is:  $x^{2} +y^{2} =36$

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:

$(x+4)^{2} +y^{2} =36$

The center of this circle would be (-4, 0) which is still on the x-axis.