Curvature of the Focal Conic in the Isotropic Plane
DOI:
https://doi.org/10.5644/SJM.06.1.10Keywords:
Isotropic plane, conic, circle of curvatureAbstract
It is shown in \cite{beba} that every focal conic $\mathcal{C}$ in the isotropic plane can be represented by the equation $y^2=\epsilon x^2+x$, $\epsilon \in \{-1,0,1\}$ and a parametrization. This paper gives the equation of the circle of curvature at the point $T$ of the focal conic $\mathcal{C}$. The radius of curvature $\rho$ at the point $T$ of the focal conic $\mathcal{C}$ is given as well as its relation to the span $\delta $ from the center of $\mathcal{C}$ to the tangent $\lijepot$ at the point $T$ and to the length of the half diameter of $\mathcal{C}$ on the diameter parallel to the $\textup{tangent}$.
2000 Mathematics Subject Classification. 51N25
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References
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