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    jianjunzhou2008's Avatar
    jianjunzhou2008 Posts: 4, Reputation: 1
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    #1

    Sep 14, 2008, 09:09 PM
    the arclength of the ellipse
    How can I find the arclength of the ellipse x^2+4y^2=1 ? Thanks in advance.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Sep 15, 2008, 05:27 AM
    Finding the arc length of ellipses can be difficult. They involve Elliptic Integrals, hence the name.

    The ellipse can be expressed parametrically:

    The total arc length of the ellipse is given by



    Where . This e means eccentricity, not to be confused with the exponential e.

    But, with yours maybe we can solve for y and use the arc length formula.

    Knowing that arc length is given by





    We could also try the polar and parametric arc length formulas:

    In parametric:

    Polar:

    There you go. There is enough info to solve it one way or another.

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