Long description: fig8

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Two graphs, (a) and (b), illustrating the shapes of hyperbolic curves with labeled features like foci and asymptotes.

Alt text: Two graphs, (a) and (b), illustrating the shapes of hyperbolic curves with labeled features like foci and asymptotes.

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  • Graph (a) shows two separate branches of a hyperbola opening horizontally along the x-axis, with dashed lines representing the asymptotes and labeled points for the foci at emoveMath{\( -ae \text{ and } ae \text{ on the x-axis}}.
  • Graph (b) shows two separate branches of a hyperbola opening vertically along the y-axis, with dashed lines representing the asymptotes and labeled points for the foci on the x-axis.

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