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Math Help - Equation of a Hyperbola

  1. #1
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    Equation of a Hyperbola

    Hello,

    Can someone please help me find the equation for this problem?

    Here are the given

    one of the points is (4,4)
    The vertices is (+/- 2sqrt(3), 0)

    The graph is plotted using this equation x^2 - y^2 = 1

    Thanks!
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  2. #2
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    are u sure the equation x^{2}-y^{2}=1 is correct?
    I plot the graph and it doesn't even pass through (4, 4)
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  3. #3
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    In the book all it shows is this graph.
    Attached Thumbnails Attached Thumbnails Equation of a Hyperbola-graph.jpg  
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  4. #4
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    The equation of a hyperbola is given by \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1, where (h, k) is the centre of the hyperbola.

    For your question, the hyperbola is centered at the origin.

    a is the distance from the centre to the vertices.

    so a=2\sqrt{3}

    Now we have \frac{x^{2}}{(2\sqrt{3})^{2}}-\frac{y^{2}}{b^{2}}=1

    Since (4, 4) is on the curve, you may substitute x=4, y=4 to find b^{2}.

    Hope this helps
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