A tangent of slope 2 of the ellipse x 2 a 2 + y 2 1 = 1 passes through - 2 , 0 . Then, three times the square of the eccentricity of the ellipse is equal to

Question

A tangent of slope 2 of the ellipse x 2 a 2 + y 2 1 = 1 passes through - 2 , 0 . Then, three times the square of the eccentricity of the ellipse is equal to,

MARKS App · Accepted Answer

A tangent of slope 2 to the ellipse x 2 a 2 + y 2 1 = 1 is y = 2 x ± 4 a 2 + 1 which passes through - 2 , 0 ⇒ 0 = 2 - 2 ± 4 a 2 + 1 ⇒ 4 a 2 + 1 = 16 ⇒ a 2 = 15 4 ⇒ e 2 = 1 - 4 15 = 11 15 ⇒ 3 e 2 = 2.2

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