I'm currently studying circle co-ordinate geometry, and this problem has puzzled me.
Find the equations of the circles of radius $5$, which touch the x-axis, and pass through the point $(3,1)$.
I would imagine if you drew this out, there would be two circles on either side. Also, because we know that they touch the x-axis, then another point A would be $(a - 5, 0)$, where $a$ is the centre of the circle.
The equations I've been using is: $r^2 = (x - a)^2 + (y - b)^2$, as well as the distance formula based on Pythagoras.
Where do I go from here?