2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 43

  • question_answer
    If m is the slope of a line which is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{\alpha }^{2}}}-\frac{{{y}^{2}}}{{{({{\alpha }^{3}}+{{\alpha }^{2}}+\alpha )}^{2}}}=1,\] then

    A) \[\left| m \right|\ge \frac{1}{2}\] 

    B)        \[\left| m \right|\ge \frac{\sqrt{3}}{2}\]

    C) \[\left| m \right|\ge 2\]    

    D)        \[\left| m \right|\ge \frac{2}{3}\]

    Correct Answer: B

    Solution :

    [b] If slope of tangent to hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is m then \[{{a}^{2}}{{m}^{2}}-{{b}^{2}}\ge 0\]. For given hyperbola \[{{\alpha }^{2}}{{m}^{2}}-{{({{\alpha }^{3}}+{{\alpha }^{2}}+\alpha )}^{2}}\ge 0\] \[\Rightarrow \,\,{{m}^{2}}\ge {{({{\alpha }^{2}}+\alpha +1)}^{2}}\Rightarrow {{m}^{2}}\ge {{\left[ {{\left( \alpha +\frac{1}{2} \right)}^{2}}+\frac{3}{4} \right]}^{2}}\Rightarrow {{m}^{2}}\ge \frac{3}{4}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner