From the attached picture we can see an ellipse of
center (2, -3)
Vertices (2, 2) and (2, -8)
C-vertices (-1, -3) and (5, -3)
Since the coordinates of the center are (h, k), then

Since the coordinates of the vertices are (h, k + a), (h, k - a), then

Since the coordinates of the co-vertices are (h + b, k) and (h - b, k), then

Since the coordinates of the foci are (h, k + c) and (h, k - c)
To find c use the relation
![\begin{gathered} c^2=a^2+b^2 \\ c^2=5^2+3^2 \\ c^2=25+9 \\ c^2=34 \\ c=\pm\sqrt[]{34} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/o9dmxv1gp3q64s6hruvmmzv7t9qrvla41k.png)
Then the foci are
![(2,-3+\sqrt[]{34})\text{ \& (2, -3-}\sqrt[]{34})](https://img.qammunity.org/2023/formulas/mathematics/college/z3hj4pirvh0k7qsspy2cldg6xwg49frtvb.png)
The correct answer is C (3rd choice)