If eccentricity of the ellipse x 2 a 2 + 1 + y 2 a 2 + 2 = 1 is 1 6 , then the ratio of the length of the latus rectum to the length of the major axis is

Question

If eccentricity of the ellipse x 2 a 2 + 1 + y 2 a 2 + 2 = 1 is 1 6 , then the ratio of the length of the latus rectum to the length of the major axis is, 5 6, 3 6, 2 3, 2 6

MARKS App · Accepted Answer

a 2 + 2 > a 2 + 1 a 2 + 1 = a 2 + 2 1 - e 2 ⇒ a 2 = 4 ⇒ a = ± 2 Hence, the required ratio is a 2 + 1 a 2 + 2 = 5 6

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