It is known that the two focuses of the hyperbola are F1, F2, one of the imaginary axes, the endpoint B, and the angle f1bf2 = 2 π / 3, so the eccentricity of the hyperbola can be obtained

It is known that the two focuses of the hyperbola are F1, F2, one of the imaginary axes, the endpoint B, and the angle f1bf2 = 2 π / 3, so the eccentricity of the hyperbola can be obtained

Let the origin be o, and the angle obf2 = π / 3 is obtained from the meaning of the title. Because the triangle obf2 is a right triangle, OB = B, of2 = C, so of2 / ob = C / b = Tan, π / 3 = radical 3, that is, C = radical 3b, the square of C = the square of 3B = 3 (the square of C-A), the square of 2C = the square of 3a is obtained by combining the similar terms, so C / a = 3 / 2, that is, e = 3 / 2