In each of the following, find the equation for the ellipse that satisfies the given conditions:

Vertices ( 5, 0), foci ( 4, 0)

Vertices (), foci ( ).

Here, the vertices are on the x-axis.a

Therefore, the equation of the ellipse will be of the form =1, where a is the semi-major axis.

Accordingly, a=5 and c = 4.

It is known that a² = b²+c².

5² = b²+4²

25 = b² + 16

b² = 25 – 16

b = = 3

Thus, the equation of the ellipse is =1 or = 1.