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Math Help - hyperbola

  1. #1
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    hyperbola

    Consider the hyperbola x^2/a^2+y^2/b^2 = D (where D is the distance between the foci). Without knowing any specific values of x or y calculate the slope of the asymptote.

    Thought: b can solved for and expressed as a complex number. Is its length in the complex plane the same as the desired length in the real plane, that is, is the length of the complex vector b the same as the distance from a focal point on the x axis to the asymptote?
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  2. #2
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    Quote Originally Posted by headache View Post
    Consider the hyperbola x^2/a^2+y^2/b^2 = D (where D is the distance between the foci). Without knowing any specific values of x or y calculate the slope of the asymptote.

    Thought: b can solved for and expressed as a complex number. Is its length in the complex plane the same as the desired length in the real plane, that is, is the length of the complex vector b the same as the distance from a focal point on the x axis to the asymptote?
    First, that is NOT a hyperbola, it is an ellipse. I am going to assume you meant x^2/a^2- y^2/b^2= D. For very, very large x and y, x^2/a^2 and y^2/b^2 will be very, very large compared with D. That means that, "approximately", or, perhaps better, "comparitively", x^2/a^2- y^2/b^2= (x/a+ y/b)(x/a- y/b)= 0. That is, the hyperbola will be close to the two lines x/a+ y/b= 0 and x/a- y/b= 0, the asymptotes. What are the slopes of those lines?
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