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Math Help - Ellispe Eccentricity error

  1. #1
    Junior Member
    Joined
    May 2009
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    Ellispe Eccentricity error

    we know
    b = a(1-e)

    and the equation for an ellipse is

    x/a + y/b = 1

    We're told the Ellipse E has equation

    x/2 + y/3 = 1

    so 9 = 4(1-e)
    4e = -5

    which you cant do, because that would be a complex number. BUT howcome you can get around this by swapping the values for a and b round. That also means that the focus has now transferred to the y axis, rather than the x, as foci as (ae,0) and now a = b?

    Thanks
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  2. #2
    Super Member malaygoel's Avatar
    Joined
    May 2006
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    India
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    An ellipse has always a major axis and a minor axis. And the foci lie on major axis.

    In your question, the major axis is y-axis and its length is 6. The minor axis is x-axis and its length is 4.

    Formula for eccentricity:
    1-e^2=\frac{b^2}{a^2}
    where b is length of minor axis
    and, a is length of major axis

    And the focus: ae where a is the length of major axis.

    The formula usually given in textbooks assume that a is the major axis whereas in your question a is the minor axis...hence we have to swap a and b
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