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I am designing a fountain for a Vegas hotel which sprays water in the shape of a hyperbola onto a screen. The hyperbolas shape is a function of several different variables. I am looking for conditions which will cause the area cast by the bottom and top parabolas to be equivalent. The parameters for the bottom shape are given, while those for the top are also given with the exception of 1 value. How do I compute the value of this unknown by root finding.

My notes up to now:

-compute area of bottom with given info

-area of top = area of bottom

- ...??

...I have a program which integrates the area with given input...but I am stuck