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The line 2x+4=1 is tangent to the hyperb...

The line `2x+4=1` is tangent to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`.
If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is ___________.

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