intersection of two hyperbolas, Algebra

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What are all of the points of intersection for these two hyperbolas?

Hyperbola 1 is centered at (-1, 829). Its foci are located at (-5.123, 829) and (3.123, 829). Everywhere along the hyperbola, the difference between the distances to the two foci is always 8.

Hyperbola 2 is centered at (99, -1021). Its foci are located at (99, -1007.252) and (99, -1034.748). Everywhere along the hyperbola, the difference between the distances to the two foci is always 26.832.

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