The discussion revolves around finding the equation of a conjugate hyperbola given its asymptotes, specifically y = +/- 2x. Participants are exploring the definitions and properties of conjugate hyperbolas in the context of their equations.
Some participants have provided equations for the conjugate hyperbolas and noted the importance of the signs in the equations. There is an ongoing exploration of how to represent both hyperbolas on a single graph, indicating a productive direction in the discussion.
Participants are considering the implications of the asymptotes on the equations of the hyperbolas and are reflecting on their earlier assumptions regarding the equations.
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:blue_soda025 said: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]?
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.)blue_soda025 said:Oops, what was I thinking when I wrote that.
So I guess I sketch two graphs for this question.