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Homework Help: Hyperbolas and Asymptotes

  1. Aug 12, 2006 #1
    How do u find the asymptotes to hyperbolas??

    what are the asymptotes to this equation?

    -x^2/4 + y^2/8 = 1

    i really need help :confused:
     
  2. jcsd
  3. Aug 12, 2006 #2

    HallsofIvy

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    Science Advisor

    Suppose x and y are very, very large. Then that "1" on the right hand side of
    [tex]-\frac{x^2}{4}+ \frac{y^2}{8}= 1[/tex]
    is very very small compared to the other two terms so the equation is approximately
    [tex]-\frac{x^2}{4}+ \frac{y^2}{8}= 0[/tex]

    Of course, [tex]-\frac{x^2}{4}+ \frac{y^2}{8}[/tex]
    factors as
    [tex](\frac{x}{2}+ \frac{y}{\sqrt{8}})(-\frac{x}{2}+\frac{y}{\sqrt{8}})[/tex]
    so for large x,y your equation is approximately
    [tex](\frac{x}{2}+\frac{y}{2\sqrt{2}})(-\frac{x}{2}+\frac{y}{2\sqrt{2}})= 0[/tex]

    Certainly if "ab= 0" then either a= 0 or b= 0. That gives you two linear equations whose graphs are close to the hyperbola for large x,y: the asymptotes.
     
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