Answer
See graph
Foci: $(0,-\sqrt{10}),(0,\sqrt{10})$
Work Step by Step
We are given the hyperbola:
$\dfrac{y^2}{9}-y^2=1$
Bring the equation to the standard form:
$\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$
$\dfrac{y^2}{9}-\dfrac{x^2}{1}=1$
The transverse axis is parallel to the $y$-axis.
Determine $h,k,a,b,c$:
$h=0$
$k=0$
$a^2=9\Rightarrow a=\sqrt 9=3$
$b^2=1\Rightarrow b=\sqrt {1}=1$
$c^2=a^2+b^2$
$c^2=9+1$
$c^2=10$
$c=\sqrt{10}$
The centre of the hyperbola is:
$(h,k)=(0,0)$
Determine the coordinates of the vertices:
$(h,k-a)=(0,0-3)=(0,-3)$
$(h,k+a)=(0,0+3)=(0,3)$
Determine the coordinates of the foci:
$(h,k-c)=(0,0-\sqrt{10})=(0,-\sqrt{10})$
$(h,k+c)=(0,0+\sqrt{10})=(0,\sqrt{10})$
Determine the asymptotes:
$y-k=\pm\dfrac{a}{b}(x-h)$
$y-0=\pm\dfrac{3}{1}(x-0)$
$y=\pm 3x$
Graph the hyperbola: