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

`x^(2) +y^(2) =36`

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.