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Math Help - Analytic Geometry: Ellipse

  1. #1
    Member looi76's Avatar
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    Analytic Geometry: Ellipse

    Question:
    Find the coordinates of the foci, the ends of the major axis and minor axis and the ends of the latus rectum.

    Attempt:

    \frac{y^2}{25} + \frac{x^2}{9} = 1

    a = 5, b = 3, c = \sqrt{a^2-b^2} \rightarrow c=\sqrt{25-9} = 4

    Foci \rightarrow (0,-4) and (0,4)
    Ends of Major axis \rightarrow (0,-5) and (0,5)
    Ends of Minor axis \rightarrow (-3,0) and (3,0)

    Ends of latus rectum:
    Left \rightarrow \left( -4,\frac{9}{5} \right) and \left( -4,-\frac{9}{5} \right)
    Right \rightarrow \left( 4,\frac{9}{5} \right) and \left( 4,-\frac{9}{5} \right)

    Is my answer right?
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  2. #2
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    Hello, looi76!

    Ya done real good!

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  3. #3
    MHF Contributor
    Grandad's Avatar
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    Ellipse

    Hello looi76
    Quote Originally Posted by looi76 View Post

    Ends of latus rectum:
    Left \rightarrow \left( -4,\frac{9}{5} \right) and \left( -4,-\frac{9}{5} \right)
    Right \rightarrow \left( 4,\frac{9}{5} \right) and \left( 4,-\frac{9}{5} \right)
    The major axis lies along the y-axis, so I think these coordinates should be the other way around: \Big(\pm\frac95, \pm 4\Big)

    Grandad
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