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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 |
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Answer» Correct Answer - 2 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` |
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