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 a^{2} = b^{2}+c^{2}.

13^{2} = b^{2}+4^{2}

169 = b^{2} + 25

b^{2} = 169 – 25

b = = 12

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

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