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    nerissa72's Avatar
    nerissa72 Posts: 3, Reputation: 1
    New Member
     
    #1

    Jan 30, 2012, 07:48 AM
    What is the vertex of 2x^2 4=4x y^2?
    What is the focus and vertices of 2x^2 4=4x y^2
    corrigan's Avatar
    corrigan Posts: 115, Reputation: 18
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    #2

    Jan 31, 2012, 12:08 AM
    I'm assuming that you mean .
    The first thing we need to do is put this in a form we can use. I can tell you from experience that this is an up-down hyperbola, because it is of the form . A left-right hyperbola would be of the form and the way you would get the foci and vertices is a little different, you would be swapping some of the x and y values. But right now we are focusing on your problem.

    So we need to make into something that looks more like:



    Then our center will be at the point ,
    vertices will be at the points and ,
    and the foci will be at the points and .
    You never said that you needed the asymptotes, but we'll do those too. They are just the lines with the equations

    and .

    Okay, enough abstract letters. Let's get to the actual problem.



    (I just divided both sides by 2).









    .

    So we have , , , and . Now we just plug in the numbers and get:

    center:

    vertices: and

    foci: and

    asymptotes: and

    I hope this helps :)

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