Question

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

(1) √3

(2) 2√3

(3)3√2

(4) 3/√2

Answer 1

Answer is (3) 3√2

Answer 2

Answer is (3) 3√2

2ae = 6 and 2a/e = 12

⇒ ae = 3 and a/e = 6

⇒ a² = 18

⇒ b² = a² - a²e² = 18 - 9 = 9

⇒ L.R = 2b²/a = (2 x 9)/3√2 = 3√2