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

Length of minor axis 16, foci (0, 6).


Length of major axis = 26; foci = ().


Since the foci are on the x-axis, the major axis is along the x-axis.


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


Accordingly, 2b =16 b = 8 and c=6.


It is known that a2 = b2+c2.


a2 = 82+62 = 64+36 =100


b = = 10


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


16
1