Consider a point F and a line l.
Let the point P be the foot of the perpendicular to l passing through F.
Let E be the ellipse with focus F, directrix l and eccentricity r.
Then E intersects the line FP at two points A and B. Assuming AP > BP, then AP/FP = 1/(1 - r), which I noticed is awfully reminiscent of the formula for the sum of an infinite geometric series. Is that a coincidence?
Let the point P be the foot of the perpendicular to l passing through F.
Let E be the ellipse with focus F, directrix l and eccentricity r.
Then E intersects the line FP at two points A and B. Assuming AP > BP, then AP/FP = 1/(1 - r), which I noticed is awfully reminiscent of the formula for the sum of an infinite geometric series. Is that a coincidence?
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