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Lots of tools exist for fitting a set a data to a straight line. How about fits to other specific conic sections? This remains an active field of research in computer vision at least as 2009. Some references that I found useful are Fitzgibbon et al 1999, Halir and Flusser 1998, O'Leary and ZsomborMurray 2004, and Harker et al 2008. For fitting data to an ellipse try using fit_ellipse.f90, for a hyperbola fit_hyperbola.f90, for a circle fit_circle.f90, and if you do not care what kind of conic is fit try using fit_nonspecific_conic.f90. These tools will generate noisy (x,y) data for any of the conic sections (an interesting problem itself!), fit the data to the specified conic, and report key attributes such as the center coordinates, foci coordinates, lengths of the semimajor and semiminor axes, rotatation angle of the conic, and so on.
Next up for these pages is a parabola specific fit to the algebraic distance (not too hard), and then geometric distance fitting for the ellipse, hyperbola, and parabola (medium hard). 


Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer coauthorship as appropriate. 
