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Topic: ellipse, mean distance from point on perimeter to a focus ?
Replies: 8   Last Post: Feb 12, 2010 5:56 PM

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Rob Johnson

Posts: 1,771
Registered: 12/6/04
Re: ellipse, mean distance from point on perimeter to a focus ?
Posted: Feb 11, 2010 6:10 AM
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In article <a36f3aaf-77d5-499b-bd30-f603613dcc8d@j6g2000vbd.googlegroups.com>,
G Patel <gaya.patel@gmail.com> wrote:
>Is the mean distance from a point on perimeter to a focus equal to the
>semi major axis length?


Yes.

Recall the "string and pins" method of drawing an ellipse, which
depends on the fact that the sum of the distances from a point on the
ellipse to the two foci of that ellipse is the major axis of that
ellipse. Since the sum of those two distances is always the major
axis, the sum of their means is the major axis. By symmetry, the
means of these distances are the same. Therefore, each is equal to
the semi-major axis.

Rob Johnson <rob@trash.whim.org>
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