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Thread: [RESOLVED] Plot ellipse through apex and two other points

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  1. Dec 26th, 2013, 09:36 PM #4
    Logophobic
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    Re: Plot ellipse through apex and two other points

    Yes. Choose any arbitrary point Q and draw line QP2. For any point A on line QP2 there exists points B and C such that |AP1| + |BP1| = |AP2| + |BP2| and |AP3| + |CP3| = |AP2| + |CP2|. For some A on QP2, points B and C coincide. Then points A and B/C are the focal points of an ellipse through points P1, P2 and P3 with point P2 being the apex of the major axis.

    I cannot prove this, but I think you'll agree with my logic here.
    Actually, I'm certain that this is not universally true. Still, there is definitely more than one ellipse here.

    Just to be clear, |AP1| is the distance from point A to point P1.
    Last edited by Logophobic; Dec 26th, 2013 at 09:48 PM.
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