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

Question

If the distance between the foci of an ellipse is 6 and the distance between its directrix is 12 , then the length of its latus rectum is, 3, 3 2, 3 2, 2 3

MARKS App · Accepted Answer

Given, 2 a e = 6 and 2 a e = 12 , directrices are x = ± a e So, a e = 6 Now, using the formula for eccentricity of an ellipse ⇒ b 2 = a 2 - a 2 e 2 = 18 - 9 = 9 ⇒ L . R . = 2 b 2 a = 2 × 9 3 2 = 3 2

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