Answer
See graph
Work Step by Step
We are given the hyperbola:
$9y^2-25x^2=225$
Bring the equation to the standard form:
$\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$
$\dfrac{9y^2}{225}-\dfrac{25x^2}{225}=1$
$\dfrac{y^2}{25}-\dfrac{x^2}{9}=1$
The transverse axis is parallel to the $y$-axis.
Determine $h,k,a,b,c$:
$h=0$
$k=0$
$a^2=25\Rightarrow a=\sqrt {25}=5$
$b^2=9\Rightarrow b=\sqrt 9=3$
$c^2=a^2+b^2$
$c^2=25+9$
$c^2=34$
$c=\sqrt{34}$
Determine the coordinates of the vertices:
$(h,k-a)=(0,0-5)=(0,-5)$
$(h,k+a)=(0,0+5)=(0,5)$
Determine the coordinates of the co-vertices:
$(h-b,k)=(0-3,0)=(-3,0)$
$(h+b,k)=(0+3,0)=(3,0)$
Determine the coordinates of the foci:
$(h,k-c)=(0,0-\sqrt{29})=(0,-\sqrt{29})$
$(h,k+c)=(0,0+\sqrt{29})=(0,\sqrt{29})$
Graph the hyperbola:
