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Math Help - 3 problems to prep me for a quiz tomorrow, help appreciated

  1. #1
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    3 problems to prep me for a quiz tomorrow, help appreciated

    We're covering conic sections, so far it's just circles ellipses and hyperbolas. I have one question regarding graphs, and two regarding Hyperbolas. I don't have any clue where to start with these, so even just telling me the basic formula would be much obliged.

    Graph the following inequality. X^2-6y^2<36

    I know for this one you just start off diving by 36, getting X squared over 36, and Y squared over 6, but after that I'm lost on how you graph it.


    Give the vertices, foci, and equations of asymptotes for the hyperbola Y^2/16- X^2/81=1

    Find an equation of the hyperbola with foci (0 +/-6) and with a difference of focal radii of 8.


    The last two Im totally stumped on.
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  2. #2
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    X^2-6y^2<36 and other hyperbolas

    [(x-h)^2 / a^2] - [(y-k)^2 / b^2] = 1 (or < 1 in this case).
    h and k are both zero in this case.

    Foci: (h +|- c, k)
    Vertices: (h +|- a, k)
    Asymptotes: (y - k) = (+|-b/a)(x-h)


    I have never drawn as an inequality, but it seems clear enough.

    If you hang around, someone might just send a picture generated by software. Otherwise, it seems reasonable to shade parts of the graph that would satisfiy the constraints, and make the boundaries dotted lines.
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