Answer
center $(0,0)$, transverse axis $y$-axis, vertices $(0,-5),(0,5)$, oci $(0,-5\sqrt {2}),(0,5\sqrt {2})$, and asymptotes $y= \pm x$.
See graph.
Work Step by Step
1. Given $y^2-x^2=25\Longrightarrow \frac{y^2}{25}-\frac{x^2}{25}=1$, we can find the center $(0,0)$, transverse axis $y$-axis, $a=b=5$, vertices $(0,-5),(0,5)$, $c=\sqrt {a^2+b^2}=\sqrt {25+25}=5\sqrt {2}$, foci $(0,-5\sqrt {2}),(0,5\sqrt {2})$, and asymptotes $y=\pm\frac{a}{b}x=\pm x$.
2. See graph.
