Through the hyperbola 2x & # 178; - Y & # 178; = 2 (letter with square) right focus make a straight line L intersect the hyperbola at two points a and B, | ab | = 4, how many straight lines satisfy the condition

Through the hyperbola 2x & # 178; - Y & # 178; = 2 (letter with square) right focus make a straight line L intersect the hyperbola at two points a and B, | ab | = 4, how many straight lines satisfy the condition

2X & sup2; - Y & sup2; = 2 = = = > X & sup2; - Y & sup2; / 2 = 1 = = = > C = √ (1 + 2) = √ 3 = = = > right focus f (√ 3,0)
If the line L ⊥ X axis, substitute x = √ 3 into X & sup2; - Y & sup2. / 2 = 1 = = = > y = ± 2,
The path = | ab | = 4, and the path is the shortest
If the line L is not ⊥ X axis, and ∵ the distance between two vertices = 2