[Solved] The line 2x + y = 1 is tangent to the hyperbola \\frac{x^2}{a^2} - \\frac{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 - - JEE (Advanced) 2010 Paper-1