Paris Pamfilos, Conic homographies and bitangent pencils,
Forum Geometricorum, 9 (2009) 229--257.

Abstract: Conic homographies are homographies of the projective plane preserving a given conic. They are naturally associated with bitangent pencils of conics, which are pencils containing a double line. Here we study this connection and relate these pencils to various groups of homographies associated with a conic. A detailed analysis of the automorphisms of a given pencil specializes to the description of affinities preserving a conic.  While the algebraic structure of the groups involved is simple, it seems that a geometric study of the various questions is lacking or has not been given much attention. In this respect the article reviews several well known results but also adds some new points of view and results, leading to a detailed description of the group of homographies preserving a bitangent pencil and, as a consequence, also the group of affinities preserving an affine conic.

[ps file][pdf]