Answer
Fill the blanks with
... $(0,-5) ... (0,5)$ ...
... $(0,-6)$ ... $(0,6)$ ...
Work Step by Step
The standard form of the equation of a hyperbola with center at the origin is
$\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\ \ $ the transverse axis lies on the x-axis
or
$\displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1 \ \ $ the transverse axis lies on the y-axis.
The vertices are $a$ units from the center and
the foci are $c$ units from the center.
For both equations, $b^{2}=c^{2}-a^{2}$.
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$\displaystyle \frac{y^{2}}{25}-\frac{x^{2}}{9}=1$
$a^{2}=25,\quad a=5$,
the transverse axis lies on the y-axis,
Vertices: $(0,-5)$ and $(0,5)$
$c^{2}=a^{2}+b^{2}$
$c^{2}=25+9=36$
$c=6$
Foci: $(0,-6)$ and $(0,6).$
Fill the blanks with
... $(0,-5) ... (0,5)$ ...
... $(0,-6)$ ... $(0,6)$ ...
