Geometric series and ellipses

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

  1. finnboltz

    finnboltz

    Joined:
    Jun 13, 2024
    Messages:
    1
    Likes Received:
    0
    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
    #1
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads

  1. Ellipses and hyperbolas of decompositions of even numbers into pairs of prime numbers.

Loading...