Answer
asymptotes: $y= \pm\frac{1}{3}x$
foci: $(0, \pm\frac{\sqrt {10}}{3})$
Work Step by Step
Step 1. From the given equation $\frac{y^2}{1/9}-\frac{x^2}{1}=1$, we have $a=\frac{1}{3}, b=1, c=\sqrt {a^2+b^2}=\frac{\sqrt {10}}{3}$ centered at $(0,0)$ with a vertical transverse axis.
Step 2. We can find the vertices as $(0,\pm\frac{1}{3})$ and asymptotes as $y=\frac{a}{b}x=\pm\frac{1}{3}x$
Step 3. We can graph the equation as shown in the figure with foci at $(0, \pm\frac{\sqrt {10}}{3})$
