How to convert a hyperbolic system to cartesian?

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To convert a hyperbolic coordinate system to Cartesian coordinates, the equations x = a exp(+u) cosh(v) and y = b exp(-u) sinh(v) are provided. The user seeks to express x and y solely in terms of u and v, without needing the coefficients a and b. Clarification is requested on how to derive these expressions without additional information on the coefficients. The discussion highlights the challenge of isolating x and y in terms of u and v while maintaining the relationship defined by the hyperbolic functions. Further assistance is needed to resolve the coefficients a and b in relation to u and v.
Bruno Tolentino
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Are you trying to solve for u and v in terms of x and y?
 
No! The oposite this! I'm trying to solve for x and y in terms of u and v!
 
Bruno Tolentino said:
No! The oposite this! I'm trying to solve for x and y in terms of u and v!
That's exactly what you already have:
x = a exp(+u) cosh(v)
y = b exp(-u) sinh(v)
 
But I want to express x and y only in terms of u and v, only! I don't know what's the coefficients a and b in terms of u and v...
 
No more answers?
 
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