[tex]\bf \textit{hyperbolas, horizontal traverse axis }
\\\\
\cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1
\qquad
\begin{cases}
center\ ( h, k)\\
vertices\ ( h\pm a, k)
\end{cases}\\\\
-------------------------------\\\\
5x^2-y^2=25\implies \cfrac{5x^2}{25}-\cfrac{y^2}{25}=1\implies \cfrac{x^2}{5}-\cfrac{y^2}{5^2}=1
\\\\\\
\cfrac{(x-0)^2}{(\sqrt{5})^2}-\cfrac{(y-0)^2}{5^2}=1\qquad
\begin{cases}
a=\sqrt{5}\\
b=5
\end{cases}[/tex]
now, the asymptotes rectangle is a rectangle that is (a+a) in width and (b+b) in length, thus its area is 2a*2b,
[tex]\bf \stackrel{2a}{2\sqrt{5}}~~\times ~~\stackrel{2b}{2\cdot 5}\implies 20\sqrt{5}[/tex]
