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 Summary

How do you calculate the equation of a hyperbola, knowing only the following:
The y intercept: (0, y)
The area bounded by x=0: A
How do you calculate the equation of a hyperbola, knowing only that the y intercept is (0,y) and the area bounded at x=0 is 'A'.
It stands to reason that this can be calculated, but I can't find a tutorial or something similar online to help me answer this.
This isn't homework, I'm just trying to further my understanding of maths particularly in regards to cosmology; but I would appreciate it if it was treated as such. I want to understand the process of how the answer is reached.
If it helps for ease of explaining we can treat the y intercept as (0,10) and the Area as 100.
It stands to reason that this can be calculated, but I can't find a tutorial or something similar online to help me answer this.
This isn't homework, I'm just trying to further my understanding of maths particularly in regards to cosmology; but I would appreciate it if it was treated as such. I want to understand the process of how the answer is reached.
If it helps for ease of explaining we can treat the y intercept as (0,10) and the Area as 100.