Matrix Representation of Conic Sections

Vertices

For a general conic we can determine its vertices by calculating the intersection of the conic and its axes — in other words, by solving the system:

$V \ \stackrel{\mathrm{def}}{=}\ \left\{\begin{matrix} & e &\qquad \mbox{(axis)} \\ & Q &\qquad \mbox{(the general equation of the conic)} \end{matrix} \right.$