On comparing the equation with the equation \(\frac{3^{2}}{a^{2}}\ -\ \frac{y^{2}}{b^{2}}=1\)
We have \(a = b = 1\) also
\(c^{2} = a^{2}\ +\ b^{2} = 1\ +\ 1 = 2\)

\(c = \sqrt{2}\) The equation of hyperbola is given by \(\frac{x^{2}}{a^{2}}\ -\ \frac{y^{2}}{b^{2}}=1\) Vertex is \((\pm\ a\ 0)\ \rightarrow\ (\pm\ 1,\ 0)\) Foci is \((\pm\ c,\ 0)\ \rightarrow (\pm\ \sqrt{2},\ 0)\) Directrix is \(x =\ \pm\ \frac{a^{2}}{c}\ =\ \pm\ \frac{1}{\sqrt{2}}\) Eccentricity \(e = \frac{c}{a} = \sqrt{2}\)

\(c = \sqrt{2}\) The equation of hyperbola is given by \(\frac{x^{2}}{a^{2}}\ -\ \frac{y^{2}}{b^{2}}=1\) Vertex is \((\pm\ a\ 0)\ \rightarrow\ (\pm\ 1,\ 0)\) Foci is \((\pm\ c,\ 0)\ \rightarrow (\pm\ \sqrt{2},\ 0)\) Directrix is \(x =\ \pm\ \frac{a^{2}}{c}\ =\ \pm\ \frac{1}{\sqrt{2}}\) Eccentricity \(e = \frac{c}{a} = \sqrt{2}\)