Solution:
The standard equation of an ellipse is expressed as

where

Step 1:
Evaluate the center (h,k) along the vertices (-2,-1) and (8, -1)
Using the midpoint formula

Step 2:
From the length of the major axis of the ellipse given as 2a, we have
![\begin{gathered} 2a=\sqrt[]{(}8-(-2))^2-(-1-(-1))^2 \\ 2a=10 \\ \Rightarrow a=5 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/q8320hxnxlo7ks03wbi081csiou29jls78.png)
Step 3:
Recall that the foci is expressed as

but

Hence, the standard form of the ellipse becomes
