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Summary:
Explicit expression are given for the coordinates of foci and vetices of quadrics in terms of the coefficients of their equations in Cartesian coordinates. Given expressions are restricted on the case of quadrics whose axes are not parallel to the coordinate axes $(a_{12}\neq 0)$. For $a_{12}=0)$, some of the expressions require a limiting process.
References:
[1] Bydžovský B. : Úvod do analytické geometrie. Praha 1923 resp. 1946.
[2] Kasner E. : The Trajectories of Dynamics. Transactions of the American Mathematical Society 7, 1906,401. MR 1500757
[3] Mišoň K. : Diferenciálně geometrické a kinematicko-geometrické modely v dynamice silových polí. - Strojnický časopis SAV, XXI, 1970, 630.
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