Answer
- the vertices are $( \pm 2,0)$
- the foci are $( \pm \sqrt{40/9},0)$
- the center is $(0,0)$
- asymptotes $y=\pm \frac{2/3}{2}(x)=\pm \frac{1}{3}x$.
Work Step by Step
The equation
$$
\left(\frac{x}{2}\right)^{2}-\left(\frac{y}{2/3}\right)^{2}=1
$$
is a hyperbola with $a=2, b=2/3$ and hence $ c=\sqrt{a^2+b^2}=\sqrt{40/9} $. So, we have
the vertices are $( \pm 2,0)$
the foci are $( \pm \sqrt{40/9},0)$
the center is $(0,0)$
asymptotes $y=\pm \frac{2/3}{2}(x)=\pm \frac{1}{3}x$.
