Answer
Ellipse.
Center: $\quad (0,0)$
Vertices: $ \quad (0,5), \quad (0,-5)$
Foci: $\quad (0,3), \quad (0,-3)$
Work Step by Step
Both variables squared, a plus between terms$\Rightarrow$ Ellipse.
Table 3:
$\begin{array}{ll}
{\text { Foci }}&{\text{Vertices}}&{\text{Equation}}\\\hline
{(h, k+c)}&{(h,k+a)}&{\displaystyle \frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}}=1}\\
{(h,k-c)}&{(h,k-a)}&{a\gt b\gt 0\text{ and }b^{2}=a^{2}-c^{2}}\end{array}$
$a=5, \quad b=4$
Find$ \quad c$ :
$c^{2}=a^{2}-b^{2}=25-16=9$
$c=3$
Center: $\quad (0,0)$
Vertices: $ \quad (h,k\pm a)=(0,\pm 5)$
Foci: $\quad (h,k\pm c)=(0,\pm 3)$
