In an ellipse the distance between the foci is 8 and the distance between the directrices is 25. Then length of major axis, is

In an ellipse the distance between the foci is $8$ and the distance between the directrices is $25$ . Then length of major axis, is

A
$10 \sqrt{2}$
B
$20 \sqrt{2}$
C
$30 \sqrt{2}$
D
none of these

Solution:

lt is given that $2 a e = 8$ and $\frac{2 a}{e} = 25$

$\Rightarrow 2 a e \times \frac{2 a}{e} = 8 \times 25 \Rightarrow 4 a^{2} = 200 \Rightarrow a = 5 \sqrt{2} \Rightarrow 2 a = 10 \sqrt{2}$ .

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