JEE Main 2024 Mathematics question
Let the latus rectum of the hyperbola subtend an angle of π/3 at the centre of the hyperbola. If b² is equal to , where ℓ and m are co-prime numbers, then ℓ² + m² + n² is equal to .
Answer: 182
Solution
The end of the latus rectum is (ae, b²/a) and each half subtends π/6, so tan(π/6) = (b²/a)/(ae) = b²/(a²e) = 1/√3, giving e = √3b²/9. With e² = 1 +
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