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Math Help - Hyperbola question

  1. #1
    s3a
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    Hyperbola question

    My teacher said this was badly worded but I still want to solve it:

    "Two megaphones shaped like trumpets are attached to the roof of a car, sending sound waves in both directions. These megaphonees were designed to follow a hyperbola with vertices at (0, 8) and (0, -8), and foci at (0, 10) and (0, -10) in a Cartesian plane. The total length of the megaphones is 96cm. What is the diameter of the trumpets?"

    The answer is: ~71cm.

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by s3a View Post
    My teacher said this was badly worded but I still want to solve it:

    "Two megaphones shaped like trumpets are attached to the roof of a car, sending sound waves in both directions. These megaphonees were designed to follow a hyperbola with vertices at (0, 8) and (0, -8), and foci at (0, 10) and (0, -10) in a Cartesian plane. The total length of the megaphones is 96cm. What is the diameter of the trumpets?"

    The answer is: ~71cm.

    Any help would be greatly appreciated!
    Thanks in advance!
    I assume those (0, 8), (0, -8), (0, 10), and (0, -10) are in centimeters also.

    You can write that hyperbola as \frac{y^2}{64}- \frac{x^2}{b^2}= 1. Further, the information about the foci tells you that 64+ b^2= 100 so b^2= 36.

    The equation of the hyperbola is \frac{y^2}{64}- \frac{x^2}{36}= 1. The radius of the trumpets is the y value when x= 96.
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