Given that point a is the left vertex of hyperbola x2-y2 = 1, point B and point C are on the right branch of hyperbola, and △ ABC is an equilateral triangle, then the area of △ ABC is___ ．

Given that point a is the left vertex of hyperbola x2-y2 = 1, point B and point C are on the right branch of hyperbola, and △ ABC is an equilateral triangle, then the area of △ ABC is___ ．

The left vertex of the hyperbola x2-y2 = 1 is a (- 1, 0). According to the symmetry of the hyperbola, let B (x1, Y1), C (x1, - Y1). From △ ABC is an equilateral triangle {AB = BC, it is obtained that: (x1 + 1) 2 + Y12 = (- y1-y1) 2, and x12-y12 = 1, ∧ x12-x1-2 = 0, ∧ X1 = - 1 or X1 = 2. The characteristic of the right branch is x ≥ 0, so X1 = 2, so Y1 = ± 3, thus a (- 1, 0), B (2, 3), C (2, - 3), We can calculate the area: S = 34ab & nbsp; 2 = 34 × [32 + (3) 2] = 33