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henpen
Are all \[y= \frac{1}{x^{2n-1}} \] hyperbolas?
I don't think so. I believe the name hyperbola is given only to one of the conic sections. It's equation can be written in one of these forms:\[\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\qquad\text{East-West Hyprbola}\]\[\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\qquad\text{North-South Hyprbola}\]\[xy=m\qquad\text{Rectangular Hyperbola}\]
Thanks- it seemed as if conic-sections-wise http://en.wikipedia.org/wiki/File:Hyperbola_(PSF).png the higher powers corresponded to moving the slicer to the right.