The equation of the ellipse in standard form with vertices along the major axis at (0, 1) and (0, -9) and the foci of the ellipse at (0, -1) and (0, -7) is (y+4)²/16 + x²/25 = 1.
The location of the center of the ellipse is the midpoint of the line segment between the ends of the major axis, that is:
(h, k) = 0.5 · (0, 1) + 0.5 · (0, -9)
(h, k) = (0, -4)
The length of the major semiaxis (b) is 5 and the distance between the center and any of the foci (c) is 3. Then, the length of the minor semiaxis is:
[tex]a = \sqrt{b^{2}-c^{2}}[/tex] (1)
a = 4
Lastly, we substitute all the variables and conclude that the equation of the ellipse is (y+4)²/16 + x²/25 = 1. [tex]\blacksquare[/tex]
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