Conjugate Hyperbola: Find Equation w/ Asymptotes y=+/-2x

[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?

 

[xanthym]

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?

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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[blue_soda025]

Oops, what was I thinking when I wrote that.

So I guess I sketch two graphs for this question.

 

[xanthym]

Oops, what was I thinking when I wrote that.

So I guess I sketch two graphs for this question.

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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