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Thread: Find the center, vertices, foci and eccentricity

  1. #1
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    Find the center, vertices, foci and eccentricity

    Find the center, vertices, foci and eccentricity of the ellipse given by the following problem.
    x^2 / 11 + y^2 / 36 =1. Did I do it right? Thanks
    Center: (0,0)
    Vertices: (0,6) and (0,-6)
    Foci: (0,5) and (0, -5)
    eccentricity= 5/6
    a^2=36 a=6
    b^2=11 b=square root of 11 = 3.32
    a^2=b^2+c^2
    36=11+c^2
    25=C^2
    c=5
    e=c/a = 5/6
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  2. #2
    Super Member bigwave's Avatar
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    Cool values of ellipse

    $\displaystyle
    \frac{\left(x - h\right)^2}{b^2} + \frac{\left(y - k\right)^2}{a^2} = 1
    \Rightarrow
    \frac{x^2}{11} + \frac{y^2}{36} = 1
    $

    major axis is parallel to the y axis
    Center is $\displaystyle (h,k)\ h=0,\ k=0,\ \Rightarrow(0,0)$
    Vertices are $\displaystyle (h,k+a)\ (h,k-a)\ 0+6,\ 0-6 \Rightarrow \pm6$
    Foci $\displaystyle (h,k+c)\ (h,k-c) \ 0,0+5\ 0,0-5 \Rightarrow (0,5)\ (0,-5)$
    eccentricty $\displaystyle \frac{e}{c}\ \Rightarrow \frac{5}{6}$
    Last edited by bigwave; May 5th 2010 at 10:20 AM. Reason: more info
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