已知A,B是双曲线y^2/a^2-x^2/a^2=1(a>0,b>0)的两个顶点,M是双曲线上的一点,若直线AM与BM的斜率之积k(AB)*k(BM)>1,则此双曲线的离心率取值范围是:()A.(1,根号2) B.(根号2,正无穷)C.(1,2) D.(2,正无穷
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![已知A,B是双曲线y^2/a^2-x^2/a^2=1(a>0,b>0)的两个顶点,M是双曲线上的一点,若直线AM与BM的斜率之积k(AB)*k(BM)>1,则此双曲线的离心率取值范围是:()A.(1,根号2) B.(根号2,正无穷)C.(1,2) D.(2,正无穷](/uploads/image/z/12540633-33-3.jpg?t=%E5%B7%B2%E7%9F%A5A%2CB%E6%98%AF%E5%8F%8C%E6%9B%B2%E7%BA%BFy%5E2%2Fa%5E2-x%5E2%2Fa%5E2%3D1%28a%3E0%2Cb%3E0%29%E7%9A%84%E4%B8%A4%E4%B8%AA%E9%A1%B6%E7%82%B9%2CM%E6%98%AF%E5%8F%8C%E6%9B%B2%E7%BA%BF%E4%B8%8A%E7%9A%84%E4%B8%80%E7%82%B9%2C%E8%8B%A5%E7%9B%B4%E7%BA%BFAM%E4%B8%8EBM%E7%9A%84%E6%96%9C%E7%8E%87%E4%B9%8B%E7%A7%AFk%28AB%29%2Ak%EF%BC%88BM%EF%BC%89%3E1%2C%E5%88%99%E6%AD%A4%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%EF%BC%9A%EF%BC%88%EF%BC%89A.%281%2C%E6%A0%B9%E5%8F%B72%29+B.%28%E6%A0%B9%E5%8F%B72%2C%E6%AD%A3%E6%97%A0%E7%A9%B7%EF%BC%89C.%EF%BC%881%2C2%29+D.%282%2C%E6%AD%A3%E6%97%A0%E7%A9%B7)
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