Answer
Fill the blanks with
... $(-5,0)$ ... $(5,0)$ ...
... $(-6,0)$ ... $(6,0)$ ...
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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$\displaystyle \frac{x^{2}}{25}-\frac{y^{2}}{9}=1$
$a^{2}=25,\quad a=5$,
the transverse axis lies on the x-axis.
Vertices: $(-5,0)$ and $(5,0)$
$c^{2}=a^{2}+b^{2}$
$c^{2}=25+9=36$
$c=6$
Foci: $(-6,0)$ and $(6,0).$
Fill the blanks with
... $(-5,0)$ ... $(5,0)$ ...
... $(-6,0)$ ... $(6,0)$ ...
