Answer
Fill the blanks with
... 5 ...
... $(0,-\sqrt{5})$ ... $(0,\sqrt{5})$
Work Step by Step
Standard form with center at $(h,k)$,
major and minor axes of lengths $2a$ and $2b$
(where $a$ and $b$ are positive, and $a^{2} > b^{2}$):
$\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$
(major axis parallel to the y-axis, vertical)
---------
Center:$ (h, k)$
Vertices: $(h, k-a),\quad (h, k+a) $
Foci are $c$ units above and $c$ units below the center, where $c^{2}=a^{2}-b^{2}$
$\displaystyle \frac{x^{2}}{4}+\frac{y^{2}}{9}=1.$
$(h,k)=(0,0)$
$a^{2}=9, b^{2}=4.$
$c^{2}=9-4=5$
$c=\sqrt{5}$
Foci:
$(0,-\sqrt{5}), (0,\sqrt{5})$
Fill the blanks with
... 5 ...
... $(0,-\sqrt{5})$ ... $(0,\sqrt{5})$
