In each of the following, find the equation for the ellipse that satisfies the given conditions:
Vertices (0, 13), foci (0, 5)
Vertices (), foci (0,).
Here, the vertices are on the x-axis.
Therefore, the equation of the ellipse will be of the form =1, where a is the semi-major axis.
Accordingly, a=13 and c = 5.
It is known that a2 = b2+c2.
132 = b2+52
169 = b2 + 15
b2 = 169 – 125
b = = 12
Thus, the equation of the ellipse is =1 or = 1.