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Math Help - Conic Sections assistance

  1. #1
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    Conic Sections assistance

    I would really appreciate your help, if anyone can give it. I'm so stuck.

    I've got a worksheet due and I've got two problems that I'm stumped on.

    1) Find the foci of a hyperbola with the equation 9y^2-72y-16x^2-64x-64=0

    2) Find the slopes of the asymptotes of a hyperbola with the equation y^2=36+4x^2.

    If you would, please explain your steps so I can understand what you're saying.

    Much appreciated
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  2. #2
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    Quote Originally Posted by ScottStedman View Post
    ...
    1) Find the foci of a hyperbola with the equation 9y^2-72y-16x^2-64x-64=0

    2) Find the slopes of the asymptotes of a hyperbola with the equation y^2=36+4x^2.

    ...
    1. Re-write the equation of the hyperbola in standard form:
    <br />
\begin{array}{l} 9y^2-72y-16x^2-64x-64=0  \\ \implies 9(y^2-8y+16)-16(x^2+4x+4)=64+144-64<br />
\\  \implies  \dfrac{(y-4)^2}{4^2} - \dfrac{(x+2)^2}{3^2}=1 \end{array}

    Now you know: The hyperbola is opening up.
    M(-2, 4)
    a = 4, b = 3
    e = \sqrt{a^2+b^2}
    F_1(-2, 4+e) , F_2(-2, 4-e)

    2. Re-write the equation in standard form. Determine the coordinates of M and the lengthes of the axes.
    The slope of the asymptotes is m_{1,2} = \pm \dfrac ba
    The asymptotes pass through M.
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