Geometric series and ellipses

Discussion in 'Geometry and Trigonometry' started by finnboltz, Jun 13, 2024.

  1. finnboltz


    Jun 13, 2024
    Likes Received:
    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?
    Last edited: Jun 13, 2024
    finnboltz, Jun 13, 2024
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