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Homework Help: Conics Question

  1. Jun 15, 2006 #1
    Hello,

    I started this problem. I dont know really how to set it up. I attached my work. I know it is wrong but I do not know where. the correct answer is 42.2.

    Here is the question:

    A bridge over a river is supported by a hyperbolic arch which is 200 m wide at the base. The maximum height of the arch is 50 m. How high is the arch at a point 30 m from the center.

    I drew a diagram (which I know is incorrect because my work assumes the center is (0,0)

    Help.

    If you have any ideas without looking at my work, anything will be appreciated. Thanks
     

    Attached Files:

  2. jcsd
  3. Jul 5, 2006 #2

    Tom Mattson

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    Gold Member

    Hi, sorry for the late response. Blame it on the summer!

    Anyway let's take a look at the standard form of the equation of a hyperbola with a vertical transverse axis.

    [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]

    You've drawn one of the vertices at the origin, which is fine. But then you set [itex](h,k)=(0,0)[/itex] which is not fine. Those are the coordinates of the center, which certainly does not coincide with either of the vertices. You've also misidentified [itex]a[/itex] and [itex]b[/itex]. They are not the distances given in the problem.

    Here's what I would do. Start from the diagram that you've drawn (with the vertex at the origin). That means that the center of the hyperbola is on the y-axis, which implies that [itex]h=0[/itex] in the above equation. Then use the 3 points on your diagram to find [itex]a[/itex], [itex]b[/itex], and [itex]k[/itex]. You have 3 points and you need to find 3 constants. That should be feasible.
     
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