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Re: ellipse, mean distance from point on perimeter to a focus ?
Posted:
Feb 11, 2010 6:10 AM


In article <a36f3aaf77d5499bbd30f603613dcc8d@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 semimajor axis.
Rob Johnson <rob@trash.whim.org> take out the trash before replying to view any ASCII art, display article in a monospaced font



