It is known that F 1 F 2 is the focus of hyperbola ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0). The chord AB passes through F 1 and the two points of a and B are on the same branch if | af2 | + | BF2 | = 2 | ab| Then the value of | ab | is

It is known that F 1 F 2 is the focus of hyperbola ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0). The chord AB passes through F 1 and the two points of a and B are on the same branch if | af2 | + | BF2 | = 2 | ab| Then the value of | ab | is

Using hyperbola to define
|AF2|-|AF1|=2a --->|AF2|=|AF1|+2a ①
|BF2|-|BF1|=2a --->|BF2|=|BF1|+2a ②
①+②
|AF2|+|BF2|=|AF1|+|BF1|+4a
∴ 2|AB|=|AB|+4a
∴ |AB|=4a