If it is possible to draw the tangent to the hyperbola `x^2/a^2-y^2/b^2=1`having slope 2,then find the range of eccentricity
Text Solution
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For the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` the tangent having slope m is `y=mx pm sqrt(a^(2)m^(2)-b^(2))`. The tangent having slope 2 is `y=2x pm sqrt(4a^(2)-b^(2))`, which is real `4a^(2)-b^(2)ge0` `"or "(b^(2))/(a^(2))le4` `"or "e^(2)-1le4` `"or "e^(2)le5` `"or "1lteltsqrt5`
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