Let x 2 a 2 + y 2 b 2 = 1 , a b be an ellipse, whose eccentricity is 1 2 and the length of the latus rectum is 14 . Then the square of the eccentricity of x 2 a 2 − y 2 b 2 = 1 is:

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Let x 2 a 2 + y 2 b 2 = 1 , a > b be an ellipse, whose eccentricity is 1 2 and the length of the latus rectum is 14 . Then the square of the eccentricity of x 2 a 2 − y 2 b 2 = 1 is:

Quantrex Academy · Accepted Answer

Correct answer: C. 3 2

Given: Length of latus rectum of ellipse is 14 . ⇒ 2 b 2 a = 14 . . . i Also, eccentricity is given as 1 2 ⇒ 1 2 = 1 − b 2 a 2 ⇒ 1 2 = 1 − b 2 a 2 ⇒ 1 2 = 1 − a 14 2 a 2 ⇒ - 1 2 = − 14 2 a ⇒ a = 14 ⇒ a 2 = 14 , b 2 = 7 Now, e H = 1 + b 2 a 2 ⇒ e H = 1 + 1 2 ⇒ e H = 3 2 ⇒ e H 2 = 3 2

Let x 2 a 2 + y 2 b 2 = 1 , a > b be an ellipse, whose eccentricity is 1 2 and the length of the latus rectum is 14 . Then the square of the eccentricity of x 2 a 2 − y 2 b 2 = 1 is:

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