gaokao 2015 Q11

gaokao · China · national-II-science 5 marks Conic sections Eccentricity or Asymptote Computation
Points $A$ and $B$ are the left and right vertices of hyperbola $E$. Point $M$ is on $E$, and $\triangle A B M$ is an isosceles triangle with vertex angle $120 ^ { \circ }$. Then the eccentricity of $E$ is
(A) $\sqrt { 5 }$
(B) $2$
(C) $\sqrt { 3 }$
(D) $\sqrt { 2 }$
Points $A$ and $B$ are the left and right vertices of hyperbola $E$. Point $M$ is on $E$, and $\triangle A B M$ is an isosceles triangle with vertex angle $120 ^ { \circ }$. Then the eccentricity of $E$ is

(A) $\sqrt { 5 }$

(B) $2$

(C) $\sqrt { 3 }$

(D) $\sqrt { 2 }$