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Image: Orthoptic locus of a circle, ellipses and hyperbolas

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Orthoptic_locus_of_a_circle,_ellipses_and_hyperbolas.gif ‎(328 × 328 pixels, file size: 933 KB, MIME type: image/gif, looped, 96 frames, 24 s)

Description: 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.
Title: Orthoptic locus of a circle, ellipses and hyperbolas
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Author: Cmapm
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