Final answer:
The standard form equation of the ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Step-by-step explanation:
The standard form equation of an ellipse is given by:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where (h,k) represents the coordinates of the center of the ellipse, 'a' is the length of the semi-major axis, and 'b' is the length of the semi-minor axis.
In this case, the center of the ellipse can be determined by finding the midpoint between the vertices, which is (-1, -8). The distance between the center and one of the vertices is the length of the semi-major axis, which is 5 units.
The distance between the center and one of the foci is the value 'c' in the equation, which is 3 units.
Substituting the given values into the equation, we get the standard form equation of the ellipse: (x+1)^2/25 + (y+8)^2/16 = 1