In the hyperbola-equation above a = |FG|/2, where FG realizes the difference of the circle radii: |R-r|, whereas b² = c² - a² = |OB|² - |OI|² and c = |OA| is half the distance of the two centers.

In the ellipse-equation above a = |R+r|/2, c = |OA|, as before, and b² = a² - c².

The two conics are orthogonal at their intersection point. In the case of two circles lying outside/inside each other there is only a hyperbola/ellipse satisfying the locus condition. Look at EllipseFromCir.html for the special case of the ellipse.

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