\begin{array}{l}
 (2e)^2  = (2\sqrt 2 )^2  + (2\sqrt 2 )^2  \\ 
 4e^2  = 16 \\ 
 e^2  = 4 \\ 
 e = 2 \\ 
  \\ 
 \varepsilon  = \frac{e}{a} = \sqrt 2  - numericki\,ekscentricitet \\ 
 a = \frac{2}{{\sqrt 2 }} = \sqrt 2  \to a^2  = 2 \\ 
  \\ 
 e^2  = a^2  + b^2  \to b^2  = e^2  - a^2  \to b^2  = 4 - 2 = 2 \\ 
  \\ 
 \frac{{x^2 }}{{a^2 }} - \frac{{y^2 }}{{b^2 }} = 1 \\ 
 \frac{{x^2 }}{2} - \frac{{y^2 }}{2} = 1 \\ 
 \end{array}