It is known that the points F1 and F2 are the left and right focal points of the hyperbola x square, a square, y square and b square = 1 respectively. The line passing through F2 and perpendicular to the X axis and If the hyperbola intersects at two points AB, if Abf1 is an acute triangle, then the value range of eccentricity of the triangle yes

It is known that the points F1 and F2 are the left and right focal points of the hyperbola x square, a square, y square and b square = 1 respectively. The line passing through F2 and perpendicular to the X axis and If the hyperbola intersects at two points AB, if Abf1 is an acute triangle, then the value range of eccentricity of the triangle yes

According to the intersection of the straight line passing through F2 and perpendicular to the X axis and the hyperbola at two points AB, we take x = C into the hyperbolic equation and get: C ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1y ^ 2 / b ^ 2 = C ^ 2 / A ^ 2-1 = B ^ 2 / A ^ 2Y ^ 2 = B ^ 4 / A ^ 2Y = ± B ^ 2 / A, then: | ab | = 2B ^ 2 / a | AF1 | = | BF2 | = 2A + B ^ 2 / a = (a ^ 2 + C ^ 2) / A, because ∠ f1ab