Geodesic
Double Tangent Circles and Focal Properties of Sphero-Conics
Journal for geometry and graphics, Tome 12 (2008) no. 2, pp. 161-169 Cet article a éte moissonné depuis la source Heldermann Verlag

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We give two proofs for the characterization of a sphero-conic as locus of points such that the absolute value of the sum or difference of tangent distances to two fixed circles is constant. The first proof is based on methods of descriptive and projective geometry, the second is purely algebraic in nature. In contrast to earlier results, our proofs remain valid in case of purely imaginary tangent distances (when the sphero-conic is enclosed by both circles). Minor modifications make the algebraic proof work in the hyperbolic plane as well.
Classification : 51M04, 51N05, 51N25
Mots-clés : Spherical geometry, sphero-conic, double tangent circle, focal property, elliptic geometry, hyperbolic geometry 
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     author = {H.-P. Schr�cker },
     title = {Double {Tangent} {Circles} and {Focal} {Properties} of {Sphero-Conics}},
     journal = {Journal for geometry and graphics},
     pages = {161--169},
     year = {2008},
     volume = {12},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2008_12_2_JGG_2008_12_2_a4/}
}
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H.-P. Schr�cker . Double Tangent Circles and Focal Properties of Sphero-Conics. Journal for geometry and graphics, Tome 12 (2008) no. 2, pp. 161-169. http://geodesic.mathdoc.fr/item/JGG_2008_12_2_JGG_2008_12_2_a4/