Geodesic
Isometric Invariants of Conics in the Isotropic Plane --- Classification of Conics
Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 017-026 Cet article a éte moissonné depuis la source Heldermann Verlag

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A real affine plane A2 is called an isotropic plane I2, if in A2 a metric is induced by an absolute figure (f, F), consisting of the line f at infinity of A2 and a point F in f. This paper gives a complete classification of the second order curves in the isotropic plane I2. Although conics in A2 have been investigated earlier, this paper offers a new method based on Linear Algebra. The definition of invariants of a conic with respect to the group of motions in I2 makes it possible to determine the type of a conic without reducing its equation to canonical form. The obtained results are summarized in an overview table. Such an approach can also be understood as an example of classifying quadratic forms in n-dimensional spaces with non-regular metric. 
@article{JGG_2002_6_1_a1,
     author = {J. Beban-Brkic},
     title = {Isometric {Invariants} of {Conics} in the {Isotropic} {Plane} --- {Classification} of {Conics}},
     journal = {Journal for geometry and graphics},
     pages = {017--026},
     year = {2002},
     volume = {6},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a1/}
}
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J. Beban-Brkic. Isometric Invariants of Conics in the Isotropic Plane --- Classification of Conics. Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 017-026. http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a1/