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

JEE Main 2022 Mathematics question

If the length of the latus rectum of the ellipse , is 4 and is the length of its major axis, then is equal to

Answer: 75

Completing the squares, , i.e. ( + 5)/4) = 1. The length of the latus rectum is $2((λ +

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Question ID VK-034444