Conic

A conic in ${\cal P}^2$ is the locus of all points ${\tt m}$ satisfying a homogeneous quadratic equation:

$$S({\tt m}) = {\tt m}^\top {\bf C} {\tt m} = 0 \, ,$$ (B10)

where ${\bf C}$ is a $3 \times 3$ symmetric matrix only defined up to scale. A conic thus depends on five independent parameters.