Question

The focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is

(a)  8/3

(b)  2/3

(c)  4/3

(d)  5/3

Answer 1

Correct option  (a)  8/3

Explanation :

 The directrix corresponding to the focus is x = 4. Therefore, the perpendicular distance of the directrix from the focus is

a/e - ae = 4

⇒ 2a - a/2 = 4

⇒ a = 8/3