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BCECE Engineering BCECE Engineering Solved Paper-2011

  • question_answer
    The angle of intersection of the curve \[y={{x}^{2}}\] and \[6y=7-{{x}^{3}}\]at \[(1,1)\] is

    A)  \[\pi /4\]                              

    B)         \[\pi /3\]                              

    C)         \[\pi /2\]                              

    D)         None of these

    Correct Answer: C

    Solution :

    \[y={{x}^{2}}\Rightarrow \frac{dy}{dx}=2x\Rightarrow {{m}_{1}}=2\,at(1,1)\] \[6y=7-{{x}^{3}}\Rightarrow 6\frac{dy}{dx}=-3{{x}^{2}}\] \[\Rightarrow \]\[\frac{dy}{dx}=-1/2\,\]at \[(1,1)\] \[\Rightarrow \]    \[{{m}_{2}}=-1/2\] \[\therefore \]      \[{{m}_{1}}{{m}_{2}}=-1\] at\[(1,1)\] \[\Rightarrow \]    \[\theta =\pi /2\]


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