how can I discribe a implicit equation for the Image of $$ f(t)=(\cosh(t),\sinh(t)), $$ knowing that this is an injective immersion? This doesn't look that hard, but I can't proceed.
Thanks in advance!
2026-03-29 17:24:36.1774805076
Implicit equation for the image of immersion $(\cosh(t),\sinh(t))$
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Observe that $x^2-y^2=1$ so your image is contained in the hyperbola. Also, since $\cosh t>0$ your image is the right branch of the above equilateral hyperbola.