If there are chords in an ellipse which are parallel, and if there is a straight line that can cross all of the midpoints of these parallel chords, are all of the midpoints in the same vertical position (same position on the y axis)?
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Your sentence is missing a verb. – Feb 22 '16 at 10:55
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@YvesDaoust Corrected – TabulaSmaragdina Feb 22 '16 at 10:56
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I still can't understand the question. Can you provide a figure ? Are you referring to conjugate diameters ? – Feb 22 '16 at 10:58
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@YvesDaoust Ok, I rephrased it, hope it's clearer now. – TabulaSmaragdina Feb 22 '16 at 11:03
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2This is the property of conjugate diameters, see e.g. http://www.solitaryroad.com/c434.html – Jean Marie Feb 22 '16 at 11:05
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The midpoints of any set of parallel chords of an ellipse will fall on a straight line segment.
To see this, think of viewing the ellipse obliquely along the major axis so it looks like a circle. The midpiints look like they're on a straight line in that view, so the line will also look straight when you view the ellipse directly from "above".
Oscar Lanzi
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