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If the major axis of a hyperbola is 2a, F1 and F2 are its two focal points, and AF1, AB and BF2 form an arithmetic sequence, then AB equals () Why?
The definition of hyperbola is bf2-bf1 = 2A, so BF2 = BF1 + 2a, and AF1, AB, BF2 become arithmetic sequence, so 2Ab = AF1 + BF2 = AF1 + BF1 + 2a, and AF1 + BF1 = AB, so 2Ab = AB + 2a, so AB = 2A
In this way, mainly combined with the definition
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