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Conjugate Hyperbola?

  1. Mar 5, 2005 #1
    What is a conjugate hyperbola? I'm asked to find the equation of the conjugate hyperbola if the asymptotes are y = +/- 2x.
    Would it be [tex]\frac{x^2}{1} + \frac{y^2}{4} = 1[/tex] or [tex]\frac{x^2}{1} + \frac{y^2}{4} = -1[/tex]?
     
  2. jcsd
  3. Mar 5, 2005 #2

    xanthym

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    You forgot the all important (-) signs!! Conjugate hyperbolas have identical asymptotes. One pair of conjugate hyperbolas having the above asymptotes is given by Eq #1 & #2:

    [tex] :(1): \ \ \ \ \frac{x^2}{1} - \frac{y^2}{4} = 1[/tex]

    [tex] :(2): \ \ \ \ \frac{x^2}{1} - \frac{y^2}{4} = -1 \ \ Or \ Equivalently \ \ \frac{y^2}{4} - \frac{x^2}{1} = 1 [/tex]



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    Last edited: Mar 5, 2005
  4. Mar 5, 2005 #3
    Oops, what was I thinking when I wrote that.

    So I guess I sketch two graphs for this question.
     
  5. Mar 5, 2005 #4

    xanthym

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    One (1) graph should suffice. Both conjugate hyperbolas fit nicely on 1 graph since 1 hyperbola will graph above-&-below the asymptotes and the other left-&-right. (They both share the same asymptotes.)


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    Last edited: Mar 6, 2005
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