Two circles of radius 1 are centered at \((4,0)\) and \((-4,0)\). How many circles are tangent to both of the given circles and also pass through the point \((0, 5)\)?
There are two circles, and they both symmetric with respect to the y-axis. One is externally tangent to both circles (so the unit circles are outside), and the other is internally tangent to both circles (so the unit circles are inside). You can draw both cases, but they're easy to understand.
