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Math Help - Ellipse

  1. #1
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    Ellipse

    The ellipse 14x^2+2x+y^2 = 1 has its center at the point (b, c) where
     b =
     c =
    The length of the major diameter of this ellipse is __
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  2. #2
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    can someone move this thread over to Calculus section, i posted this in the wrong section.
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  3. #3
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    14x^{2}+2x+y^{2}=1

    Complete the square and get:

    14(x+\frac{1}{14})^{2}+y^{2}=\frac{15}{14}

    \frac{196(x+\frac{1}{14})^{2}}{15}+\frac{14y^{2}}{  15}=1

    To find the x intercepts, set y=0 and solve for x, getting x=(\frac{-(\sqrt{15}+1)}{14},\frac{\sqrt{15}-1}{14})

    The center is at (-1/14,0)

    b=\frac{-1}{14}+\frac{\sqrt{15}-1}{14}=\frac{\sqrt{15}}{14}

    Setting y=-1/14 in the equation gives us major axes of a=(\frac{\sqrt{210}}{14}, \frac{-\sqrt{210}}{14})

    The foci, c, can be found by c^{2}=a^{2}-b^{2}

    c=\sqrt{(\frac{\sqrt{210}}{14})^{2}-(\frac{\sqrt{15}}{14})^{2}}=\pm\frac{\sqrt{195}}{1  4}
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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