engleski

Curve of Foci of Pencil of Conics in Pseudo-Euclidean Plane

A focus of an algebraic curve in the Euclidean plane is defined as an intersection of the isotropic tangents of the curve. The curve of class m has m2 foci. An analogous definition is valid in the Pseudo-Euclidean plane. The pencils of point conics and line conics are studied on a model of PE-plane. Their curves of foci are constructed. It is shown that the curve of foci of the pencil of point conics is of order six. It has different degrees of circularity depending on the type of the pencil. It can be entirely circular as well. Some special cases that are not possible in the Euclidean plane are pointed out. The curve of foci of the pencil of line conics is circular cubic. It can happen to be entirely circular, which is not possible in the Euclidean case. Besides the curves of foci, for the same pencils of conics the curves of centers are constructed as well.

focus of an algebraic curve; pseudo-Euclidean plane; pencils of conics

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