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Math Help - Ellipse Help

  1. #1
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    Ellipse Help

    I am given 100 x-y (cartesian) coordinates for an ellipse. The ellipse slopes upward to the northeast and is centered off the origin at a given coordinate (h, k). I need to find the two vertices (x-y coordinates) of the major axis. Can you tell me how to do this using only the information supplied? Thanks.
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  2. #2
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    Hello, sgorman!

    I am given 100 x-y (cartesian) coordinates for an ellipse.
    The ellipse slopes upward to the northeast and is centered at (h, k).
    I need to find the two vertices (x-y coordinates) of the major axis.
    Can you tell me how to do this using only the information supplied?
    I can suggest an approach ... a rather long and tedious one.

    The general quadratic function is: . Ax^2 + Bxy + Cy^2 + Dx + Ey + F \;=\;0

    Use any six of the given points and set up a 6-by-6 system of equations.
    . . Then solve for A,B, C, D, E, F

    Once we have the equation of the ellipse, we can determine the angle
    . . through which it is rotated and then the endpoints of its major axis.

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  3. #3
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    Thank you for the response. Could you give me an example of how you would set up (and solve) each of the six equations using a hypothetical set of x-y coordinates? I don't mind the tedium -- I'm just not sure how this produces the answers I need.
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  4. #4
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    I'm all set now -- thanks.
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