Someone pls i have no idea what’s going on lol (picture posted)

You have probably been shown the pattern for the equation of an ellipse. It looks something like

where (h, k) is the center of the ellipse and "a" and "b" are the semi-axes in the x- and y-directions, respectively.

In this problem, you are expected to compute h, k, a, b from the given information.

The center (h, k) is halfway between the given vertices, so will be
.. ((-5, -2) +(-5, 14))/2 = ((-5-5)/2, (-2+14)/2) = (-5, 6)

Now, you know the numerators look like
.. (x +5)^2
.. (y -6)^2

The given vertices have the same x-coordinate, so the axis in the y-direction has length (14 -(-2)) = 16. Half that value is the value of "b". It is 8.

The remaining value you need to find is that of "a". You do that using all the information you have so far to fill in the values in the equation. The given point is used for the values of x and y.
.. (0 +5)^2/a^2 +(6 -6)^2/8^2 = 1
.. 25/a^2 +0 = 1
It is pretty clear that a=5.

Now, you have all the information to fill in your form.