This is an updated version of a video that we had posted a couple of days ago. The only change is the mention of 2, not one, axes of symmetry for the image of each hyperbola under the reciprocal map.
Old Description (which still applies): We apply the reciprocal map R(z) = 1/z to two hyperbolas and determine the shape of the graphs of the image of each hyperbola under the reciprocal map.
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Hyperbolas and the Reciprocal Map on the Extended Complex Plane | NatokHD