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The symmetry of a hyperbola with a center at (h, k) only occurs at x = h. Just making sure this is false. My teacher gave us one of those practice guides with a few questions at the end.
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symmetry for a hyperbola i think only occurs at for lines which are orientated 45 degrees to the direction of the asymptotes and pass directly through the focal point of the asymptotes
so i guess at a constant x value would be one of the reflections, but at a variable x value and a constant k value would be the other symmetrical reflection
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