Q. 15

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

Length of major axis 26, foci ( 5, 0)

Answer :

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.


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