(5, 12), and (24, 7) are the foci of an ellipse which is passing through the origin, then its eccentricity is

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$\frac{\sqrt{386}}{38}$

$\frac{\sqrt{386}}{25}$

$\frac{\sqrt{386}}{20}$

$\frac{\sqrt{386}}{45}$

answer is A.

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Detailed Solution

$S (5, 12) S^{1} (24, 7) P (0, 0) W e k n o w t h a t SP + S^{1} P = 2 a \Rightarrow 2 a = 13 + 25 = 38 a n d {SS}^{1} = 2 ae = \sqrt{361 + 25} e = \frac{\sqrt{386}}{38}$

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