Question

If distance between the foci of an ellipse is 6 and distance between its directrices is 12, then length of its latus rectum is 

(1) 4

(2) 3√2

(3) 9

(4) 2√2

Answer 1

Answer is (2)

2ae = 6 and 2a/e = 12

⇒ ae = 3 and a/e = 6

⇒ a² = 18

⇒ b² = a² - a²e² = 18 - 9 = 9