Homework Help: Conjugate Hyperbola?

1. Mar 5, 2005

blue_soda025

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 $$\frac{x^2}{1} + \frac{y^2}{4} = 1$$ or $$\frac{x^2}{1} + \frac{y^2}{4} = -1$$?

2. Mar 5, 2005

xanthym

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:

$$:(1): \ \ \ \ \frac{x^2}{1} - \frac{y^2}{4} = 1$$

$$:(2): \ \ \ \ \frac{x^2}{1} - \frac{y^2}{4} = -1 \ \ Or \ Equivalently \ \ \frac{y^2}{4} - \frac{x^2}{1} = 1$$

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Last edited: Mar 5, 2005
3. Mar 5, 2005

blue_soda025

Oops, what was I thinking when I wrote that.

So I guess I sketch two graphs for this question.

4. Mar 5, 2005

xanthym

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