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Math Help - how calculate chord length of ellipse.

  1. #1
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    how calculate chord length of ellipse.

    An ellipse
    major axis: 900
    minor axis: 450
    Two points on ellipse 150 and 250 distance
    away from center line as shown in attached file (chord length)
    Then how to measure the lenght of chord AB as shown in
    attached file ?
    Attached Thumbnails Attached Thumbnails how calculate chord length of ellipse.-chord-length.jpg  
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  2. #2
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    Quote Originally Posted by ashvin123 View Post
    An ellipse
    major axis: 900
    minor axis: 450
    Two points on ellipse 150 and 250 distance
    away from center line as shown in attached file (chord length)
    Then how to measure the lenght of chord AB as shown in
    attached file ?
    If you are allowed to use a convenient coordinate system you can calculate the coordinates of the points A and B. Afterwards use the distance formula.

    Put the origin of the coordinate system on the center of the ellipse. The equation of the ellipse becomes:

    \dfrac{x^2}{450^2} + \dfrac{y^2}{225^2}=1

    Plug in x = 150 to get y = 150 \sqrt{2} .
    Thus A(150, 150\sqrt{2}) and B(250, 50 \sqrt{14})

    Now use the distance formula.
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  3. #3
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    Thank you.
    Thank you very much.
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