  A perturbative approach is used to quantify the effect of noise in data
points on fitted parameters in a general homogeneous linear model, and the
results applied to the case of conic sections. There is an optimal choice of
normalisation that minimises bias, and iteration with the correct reweighting
significantly improves statistical reliability. By conditioning on an
appropriate prior, an unbiased type-specific fit can be obtained. Error
estimates for the conic coefficients may also be used to obtain both bias
corrections and confidence intervals for other curve parameters.
