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### Hyperbolic Functions

Food for thought

Approach 1 gave the cartesian equation $x=a\ln\left(\frac{a+\sqrt{a^2-y^2}}{y}\right)-\sqrt{a^2-y^2}.$
Approach 2 gave the parametric form $\left(t-a\tanh\Bigl(\frac{t}{a}\Bigr), a\sech\Bigl(\frac{t}{a}\Bigr)\right).$