Answer
center $(0,0)$, transverse axis $x$-axis, vertices $(-2,0),(2,0)$, foci $(-2\sqrt {2},0),(2\sqrt {2},0)$, and asymptotes $y=\pm x$.
See graph.
Work Step by Step
1. Given $x^2-y^2=4\Longrightarrow \frac{x^2}{4}-\frac{y^2}{4}=1$, we can find the center $(0,0)$, transverse axis $x$-axis, $a=b=2$, vertices $(-2,0),(2,0)$, $c=\sqrt {a^2+b^2}=\sqrt {4+4}=2\sqrt {2}$, foci $(-2\sqrt {2},0),(2\sqrt {2},0)$, and asymptotes $y=\pm\frac{b}{a}x=\pm x$.
2. See graph.
