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Math Help - analytoc geometry problem! help

  1. #1
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    analytoc geometry problem! help

    Find the equation of the ellipse which crosses the point (-3,1) , and the multiply of the two distances between the point and the two focuses (foci) of the ellipse equals 6
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: analytoc geometry problem! help

    For simplicity, let's assume the major axis lies along the x-axis, where the foci are at (-c,0) and (c,0), and 0<c.

    If the product of the distances from the point (-3,1) to the foci is 6, then we may state:

    \sqrt{(-3-(-c))^2+(1-0)^2}\sqrt{(-3-c)^2+(1-0)^2}=6

    \sqrt{(3-c)^2+1}\sqrt{(3+c)^2+1}=6

    Squaring gives:

    ((3-c)^2+1)((3+c)^2+1)=36

    Now solve this for c^2.

    Next, the equation of the ellipse may be written:

    \frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1

    Since the ellipse passes through (-3,1), we may write:

    \frac{(-3)^2}{a^2}+\frac{1^2}{a^2-c^2}=1 where c^2<a^2.

    Using the value you found for c^2, you may now solve for a^2 to find the equation of the ellipse.
    Last edited by MarkFL; January 18th 2013 at 11:29 AM.
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    Re: analytoc geometry problem! help

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