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  1. #1

    Jul 2012
    5,302


    area of ellipse






    suppose semimajor axis of ellipse = a , and semiminor axis = b


    The parametric formula of ellipse :

    y = b*sin j
    x = a*cos j

    area of one - quarter of ellipse = INT (0 to a ) y.dx

    dx = - a*sin j dj
    when x = 0 ..... j = pi/2
    when x = a ..... j = 0

    area = 4*INT (from j = pi/2 to j = 0) - b*a*sin^2 j .dj

    area = 4*INT (from j = 0 to j = pi/2)* a*b (1 - cos 2j)/2 . dj

    area = 2*a*b [j - 1/2*sin 2j]from j = 0 to j = pi/2

    area = 2*a*b [pi/2 - 0 - 1/2*sin pi + 1/2*sin 0

    area = pi*a*b
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  2. #2

    Jul 2012
    5,302

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    hyperbola







    Parabola










  3. #3

    Jul 2012
    5,302

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    :











    -








  4. #4

    Jul 2012
    5,302

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    f-77




    / hoor_dana

















  5. #5
      Eiman
    Jul 2011
    -
    14,750

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