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Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    The value\[P\]such that the length of subtangent and subnormal is equal for the curve\[{{y}^{2}}={{e}^{Px}}+Px\]at the point\[(0,\,\,1)\]is

    A) \[P=\pm 1\]      

    B)        \[P=\pm 2\]

    C) \[P=\pm \frac{1}{2}\]    

    D)         None of these

    Correct Answer: C

    Solution :

    \[\frac{dy}{dx}=P{{e}^{px}}+P\] \[{{\left( \frac{dy}{dx} \right)}_{(0,\,\,1)}}=2P\] Subtangent\[=\left| y\frac{dx}{dy} \right|\], subnormal\[=\left| y\frac{dy}{dx} \right|\] Given; Subtangent = Subnormal \[\Rightarrow \]\[\frac{dy}{dx}=\pm 1\,\,\Rightarrow \,\,2p=\pm 1\]  \[\Rightarrow \]  \[p=\pm \frac{1}{2}\]


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