JEE Main 2024 Mathematics question
Let f(x) = x² + 9, g(x) = x/(x − 9) and a = fog(10), b = gof(3). If e and ℓ denote the eccentricity and the length of the latus rectum of the ellipse x²/a + y²/b = 1, then 8e² + ℓ² is equal to
Answer: (B)
Solution
g(10) = 10, so a = f(10) = 109. f(3) = 18 and b = g(18) = 18/9 = 2. The ellipse is x²/109 + y²/2 = 1 with e² = 1
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