The focus of an ellipse is at the origin. The directrix is the line x = 4 and its eccentricity is 1/2 then length of its semi major axis is (A) 2/3 (B) 4/3 (C) 5/3 (D) 8/3

Given

Directrix is x = 4

Eccentricity = 1/2

Directrix = [(a/e) – ae] = 4

(a/e) – ae = 4

a [(1/e) – e] = 4

a [2 – (1/2)] = 4

a x 3/2 = 4

We get,

a = 8/3

Hence, the correct option is (D)

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