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2015年全国高考数学新课标Ⅱ卷理科第(11)题:M是双曲线E:x2/a2-y2/b2=1(a>0,b>0)上的一点,A、B是双曲线E的左、右顶点,△MAB是等腰三角形,且顶角是120°,则双曲线E的离心率是()(A)5~1/2(B)2(C)3~1/2(D)2~1/2该问题反映了有心圆锥曲线上的一点和左、右两个顶点组成的三角形的内角或两条边斜率的积与离心率的关系,设计新颖,别具一格,作为选择题的第(11)题,难易适中,值得我们深入研究.
(11): M is a point on hyperbolic E: x2 / a2-y2 / b2 = 1 (a> 0, b> 0), A and B are double The left and right vertices of the curve E, the △ MAB is an isosceles triangle, and the apex angle is 120 °, the eccentricity of the hyperbola E is 5 to 1/2 (B) 2 (C) 3 to 1 / 2 (D) 2 ~ 1/2 This question reflects the relationship between the product of eccentricity and the product of the inner angle or the slope of two sides of a triangle formed by one point on the cone conic curve and two left and right vertices. The design is novel and unique. As a multiple choice question (11), easy to moderate, it is worth our in-depth study.