Geodesic
Explicit expressions for the coordinates of foci and vertices of a quadric in dependence on the coefficients of its Cartesian equations
Applications of Mathematics, Tome 16 (1971) no. 3, pp. 215-219
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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.
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.
DOI : 10.21136/AM.1971.103347
Classification : 65A05, 65B99 
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Mišoň, Karel. Explicit expressions for the coordinates of foci and vertices of a quadric in dependence on the coefficients of its Cartesian equations. Applications of Mathematics, Tome 16 (1971) no. 3, pp. 215-219. doi: 10.21136/AM.1971.103347

[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

[3] Mišoň K. : Diferenciálně geometrické a kinematicko-geometrické modely v dynamice silových polí. - Strojnický časopis SAV, XXI, 1970, 630.

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