JEE Main & Advanced JEE Main Solved Paper-2014

  • question_answer
    The slope of the line touching both the parabolas \[{{y}^{2}}=4x\]and \[{{x}^{2}}=-32y\]is :   JEE Main  Solved  Paper-2014

    A) \[\frac{1}{2}\]   

    B) \[\frac{3}{2}\]

    C) \[\frac{1}{8}\]                                   

    D) \[\frac{2}{3}\]

    Correct Answer: A

    Solution :

                    Now tangent with slope ?m? to \[{{y}^{2}}=4x\]is\[y=mx+\frac{1}{m}\]                                 ?(1) Also tangent with slope ?m? to\[{{x}^{2}}=-32y\]is \[y=mx+\frac{1}{m}\]                                                    ?(2) If (1) and (2) are equations of the same line then their coefficients should match. \[\Rightarrow \]\[8{{m}^{2}}=\frac{1}{m}\]\[\Rightarrow \]\[m=\frac{1}{2}\]

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