过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0)作圆:x^2+y^2=a^2/4的切线,切点为E ,直线FE交双曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为( )
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![过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0)作圆:x^2+y^2=a^2/4的切线,切点为E ,直线FE交双曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为( )](/uploads/image/z/14611164-60-4.jpg?t=%E8%BF%87%E5%8F%8C%E6%9B%B2%E7%BA%BFx%5E2%2Fa%5E2-y%5E2%2Fb%5E2%3D1%EF%BC%88a%EF%BC%9E0%2Cb%EF%BC%9E0%EF%BC%89%E7%9A%84%E5%B7%A6%E7%84%A6%E7%82%B9F%EF%BC%88-c%2C0%EF%BC%89%EF%BC%88c%3E0%29%E4%BD%9C%E5%9C%86%EF%BC%9Ax%5E2%2By%5E2%3Da%5E2%2F4%E7%9A%84%E5%88%87%E7%BA%BF%2C%E5%88%87%E7%82%B9%E4%B8%BAE+%2C%E7%9B%B4%E7%BA%BFFE%E4%BA%A4%E5%8F%8C%E6%9B%B2%E7%BA%BF%E5%8F%B3%E6%94%AF%E4%BA%8E%E7%82%B9P%2C%E8%8B%A5%E5%90%91%E9%87%8FOE%3D1%2F2%28%E5%90%91%E9%87%8FOF%2B%E5%90%91%E9%87%8FOP%29%2C%E5%88%99%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA%EF%BC%88+%EF%BC%89)
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