SVG redraw of Apollonian circles.png.  A hyperbolic transformation is shown.  Pre-images of the unit circle are circles of Apollonius with distance ratio =ca{\displaystyle ={\frac {c}{a}}} and foci at −b/a and −d/c . For the same foci −b/a and −d/c the red circles map to rays through the origin.
Own work based on: Apollonian circles.png
WillowW (original); Pbroks13 (redraw)