If then the point lies on both circles. In that case, the circles intersect, so one of them cannot lie inside the other. Conclusion: c must be greater than 0.

So now assume that c>0. Check that in this case, neither circle contains any points on the y-axis. So each circle (and its interior) lies entirely on one side of the y-axis. Your next step is to find where the centres of the circles are. If they are on opposite sides of the y-axis then neither circle can lie inside the other. So the centres must lie on the same side of the y-axis. Deduce that and have the same sign and therefore .