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If the length of the latus rectum of the ellipse x 2 + 4 y 2 + 2 x + 8 y - λ = 0 is 4 , and l is the length of its major axis, then λ + l is equal to _____.

Correct answer

0

Step-by-step solution

Given, x 2 + 4 y 2 + 2 x + 8 y - λ = 0 is a ellipse Now on rearranging the terms we get, ⇒ x + 1 2 λ + 5 + y + 1 2 λ + 5 4 = 1 We know that length of latus rectum is 2 b 2 a = 4 So, 2 λ + 5 4 λ + 5 = 4 ⇒ 2 λ + 5 4 = 4 λ + 5 ⇒ λ + 5 = 8 λ + 5 ⇒ λ + 5 2 = 64 λ + 5 ⇒ λ 2 + 25 + 10 λ = 64 λ + 5 ⇒ λ 2 - 54 λ - 295 = 0 ⇒   λ = 59   or  - 5 But λ ≠ - 5 So, l = 2 a = 2 &#9

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