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Hyperbola problem

  1. Jun 12, 2009 #1
    Two radar stations, situated 100 km apart, detect a moving airplane. The difference in the distances between the airplane and the radar stations is 50 km. Assume that the radar stations are on the y-axis, centered about the origin.

    Determine the equation of the hyperbolic path of the airplane.

    My Answer:

    2c = 100
    c = 50

    2a = 50
    a = 25

    c^2 = a^2 + b^2
    50^2 = 25^2 + b^2
    b^2 = 2500 - 625
    b^2 = 1875

    y^2 / 625 - x^2 / 1875 = 1 (or alternatively x^2 / 1875 - y^2 / 625 = -1)

    Is my answer correct? I believe I have solved the problem correctly but I wanted to double check that I understood this properly.
     
  2. jcsd
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