The line `2x + y = 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

Answer

2

Explanation

Substituting `(a/e,0)` in `y=-2x+1`
`0=-(2a)/e+1impliesa=e/2`
Also `1=sqrt(a^(2)m^(2)-b^(2))`
`1=a^(2)m^(2)-b^(2)`
`implies 1=4a^(2)-b^(2)implies1=(4e^(2))/4-b^(2)`
`b^(2)=e^(2)-1`
`h^(2)=a^(2)(e^(2)-1)impliesa=1,e=2`