Hello, sam1234!
The centres of two circles lie on the line
Both circles touch the xaxis and contain the point
Find the equations of the two circles. Code:

*  * * *
* *  *
*  *
* *  *
*
*  * C *
*  o (h,k) *
*  : * *
 : *
*  :k * o P(6,2)
*  : *
*++**
 * * * *

The center is , which lies on
. . Hence: . .[1]
The circle is tangent to the axis, so the radius is
The equation is: .
Since is on the circle: . .[2]
Substitute [1] into [2]: .
Then: .
. . Hence: .
Therefore: .