(2,4) and (10,10) are the ends of the latus rectum of an ellipse with eccentricity 1/2. The length of major axis is

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$\frac{20}{3}$

$\frac{40}{3}$

$\frac{25}{3}$

$\frac{80}{3}$

answer is B.

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Detailed Solution

$e = \frac{1}{2} \frac{2 b^{2}}{a} = L . L . R = \sqrt{36 + 64} = 10 2 b^{2} = 10 a b^{2} = 5 a a^{2} (1 - e^{2}) = 5 a a (1 - \frac{1}{4}) = 5 \Rightarrow a = \frac{20}{3} Length major ax i s = 2 a = \frac{40}{3}$

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