linguistic:translation
Implicit representation

Solving the parametric representation for cosh t, sinh t {\displaystyle \cosh t,\sinh t} by Cramer's rule and using cosh 2 t − sinh 2 t − 1 = 0 {\displaystyle \;\cosh ^{2}t-\sinh ^{2}t-1=0\;}, one gets the implicit representation det (x → − f → 0, f → 2) 2 − det (f → 1, x → − f → 0) 2 − det (f → 1, f → 2) 2 = 0. {\displaystyle \det \left({\vec {x}}\!-\!{\vec {f}}\!_{0},{\vec {f}}\!_{2}\right)^{2}-\det \left({\vec {f}}\!_{1},{\vec {x}}\!-\!{\vec {f}}\!_{0}\right)^{2}-\det \left({\vec {f}}\!_{1},{\vec {f}}\!_{2}\right)^{2}=0.}