It is known that F1F2 is the left and right focus of hyperbola x2 / a2-y2 / B2 = 1 (a > 0, b > 0), the line passing through point F1 and perpendicular to the real axis and the two asymptotes of hyperbola If the coordinate origin o is just the vertical center of △ abf2 (the intersection of the three high lines of the triangle), then the eccentricity of the hyperbola is
Because MF2 is perpendicular to the X axis, MF2 is the length of half path, and the path length of hyperbola is 2B ^ 2 / A, so MF2 = B ^ 2 / A. in the right triangle f1f2m, tan30 ° is MF2 / F1F2, so (b ^ 2 / a) / 2C = radical 3 / 3
The result is: root 3 (C ^ 2-A ^ 2) - 2Ac = 0, if both sides divide by a ^ 2 at the same time, there is: root 3E ^ 2-2e-root 3 = 0, the solution is: e = root 3