File:Orthoptic locus of a circle, ellipses and hyperbolas.gif
| Uploaded by | Cmapm |
|---|---|
| Upload date | 2012-09-21T16:53:04Z |
| MIME type | image/gif |
| Dimensions | 328 × 328 px |
| File size | 932.9 KB |
Summary
| Description |
English: Orthoptic locus (red circle) of a circle (e=0), ellipses (e<1) and hyperbolas (e>1) for different eccentricities. For a circle and an ellipse orthoptic locus is a circle, and for a hyperbola with eccentricity less than a square root of two it is a circle except four points of intersections with hyperbola's asymptotes (light blue lines). Foci are in magenta, semi-major axis a=4. See problem 27 on page 64 of the following book: A.V.Pogorelov. Geometria. Moskva:Nauka, 1983. See also here. Русский: Геометрическое место (красная окружность) вершин прямых углов, стороны которых касаются данной окружности, эллипса или гиперболы при различных значениях эксцентриситета. Для гиперболы с эксцентриситетом, меньшим, чем квадратный корень из двух, это место — окружность без четырёх точек её пересечения с асимптотами (голубые линии). Фокусы выделены фиолетовым, большая полуось a=4. См. упражнение 27 на стр. 64 следующей книги: А.В.Погорелов. Геометрия. Москва:Наука, 1983. |
| Date | |
| Source | Own work |
| Author | Cmapm |
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