The right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is F. if there is only one straight line passing through point F and inclination angle 30 and hyperbola The right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is F. if there is only one intersection point between the straight line passing through point F and hyperbola with inclination angle of 30, the range of eccentricity of hyperbola is smaller

The right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is F. if there is only one straight line passing through point F and inclination angle 30 and hyperbola The right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is F. if there is only one intersection point between the straight line passing through point F and hyperbola with inclination angle of 30, the range of eccentricity of hyperbola is smaller

k=tan30=√3/3
Let the linear equation: y = √ 3 (x-C) / 3
Then: x ^ 2 / A ^ 2 - (x-C) ^ 2 / 3B ^ 2 = 1
3(c^2-a^2)x^2-a^2(x-c)^2=3a^2(c^2-a^2)
(3c^2-4a^2)x^2+2a^2cx-4a^2c^2+3a^4=0
There is only one intersection
3c^2-4a^2=0,c^2/a^2=4/3,e=c/a=2√3/3
or
Discriminant △ = 4A ^ 4C ^ 2-4 (3C ^ 2-4a ^ 2) (3a ^ 4-4a ^ 2C ^ 2)
=48a^2(c^4+a^4-2a^2c^2)
=48a^2(a^2-c^2)^2
=0
a^2=c^2
Not established
Therefore, the hyperbolic eccentricity e = 2 √ 3 / 3