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The following picture is from the Wikipedia article on Möbius transformation.

It is explained under the picture that

Pre-images of the unit circle are circles of Apollonius with distance ratio $c/a$ 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.

I don't understand what this means. Would anyone elaborate how is this picture formed and how it is related to the Möbius transformation?

enter image description here

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    The illustration is not particularly useful. Each blue circle corresponds to exactly one Möbius transformation that transforms the blue circle to the unit circle. Each of the red circles corresponds to multiple Möbius transformations that map the circle to a ray through 0. – 2017-02-13
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    commented out the image on https://en.wikipedia.org/wiki/M%C3%B6bius_transformation#Decomposition_and_elementary_properties – 2017-03-16

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