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Math Help - find equation of ellipse????

  1. #1
    Member sluggerbroth's Avatar
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    find equation of ellipse????

    foci (0, +/- 4/3), contains (4/5,1)
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  2. #2
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    Re: find equation of ellipse????

    Quote Originally Posted by sluggerbroth View Post
    foci (0, +/- 4/3), contains (4/5,1)
    centered at the origin (why?)

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

    c = \frac{4}{3}

    b^2 = a^2 + c^2

    same drill ... sub in x and y, solve for a^2 and b^2
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  3. #3
    Member sluggerbroth's Avatar
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    Re: find equation of ellipse????

    algera gets really, really messy??? or am i doing something wrong?????
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  4. #4
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    Re: find equation of ellipse????

    yes, this one is messy ...

    \frac{(4/5)^2}{a^2} + \frac{1^2}{b^2} = 1

    b^2 = a^2 + \frac{16}{9}

    \frac{16}{25a^2} + \frac{1}{b^2} = 1

    \frac{16}{25a^2} + \frac{1}{a^2 + \frac{16}{9}} = 1

    \frac{16}{25a^2} + \frac{9}{9a^2 + 16} = 1

    16(9a^2+16) + 9(25a^2} = 25a^2(9a^2+16)

    144a^2 + 256 + 225a^2 = 225a^4 + 400a^2

    0 = 225a^4 -31a^2 - 256

    0 = (225a^2-256)(a^2 + 1)

    a^2 = \frac{256}{225}

    sometimes you just have to grind it out
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