JEE Main 2024 Mathematics question
Let H : = 1 be the hyperbola, whose eccentricity is √3 and the length of the latus rectum is 4√3. Suppose the point (α, 6), α > 0 lies on H. If β is the product of the focal distances of the point (α, 6), then α² + β is equal to:
Answer: (B)
Solution
For this hyperbola e² = 1 + a²/b² = 3 gives a² = 2b², and the latus rectum 2a²/b = 4b = 4√3 gives b = √3, a² = 6. The point (α,
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