The example below is a case where the two circles (d) and (d') are not tangent to the conic (blue ellipse) generated by the above recipe.

Points {V,W} are the homothety centers of the two circles (d) and (d'). Circle (f) has these two points as diametral points. F is always on this circle. The resulting conic for such a configuration, where one of the circles (d') is totally inside the other, is always an ellipse. The ellipse may contact or not the smaller circle (d').

A clue for the behavior of the ellipse regarding its contact with circle (d') may give the picture contained in DistanceFunction.html .

ConicsAndSimilarities.html

ConicsAndSimilarities3.html

Hyperbola.html

Similarity.html

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