In each of the following, find the equation for the ellipse that satisfies the given conditions:
Length of major axis 26, foci ( 5, 0)
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, 2a =26 a = 13 and c=5.
It is known that a2 = b2+c2.
132 = b2+42
169 = b2 + 25
b2 = 169 – 25
b = = 12
Thus, the equation of the ellipse is =1 or = 1.