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BCECE Engineering BCECE Engineering Solved Paper-2006

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

    A) \[\frac{\pi }{4}\]                              

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

    C)  \[\frac{\pi }{2}\]                             

    D)         none of these

    Correct Answer: C

    Solution :

    Given equation of curves are \[y={{x}^{2}}\]and \[6y=7-{{x}^{3}}.\] \[\ \therefore \]               \[{{m}_{1}}={{\left( \frac{dy}{dx} \right)}_{(1,1)}}=2(1)=2\] and        \[{{m}_{2}}={{\left( \frac{dy}{dx} \right)}_{(1,1)}}=-\frac{1}{2}\] Now, \[{{m}_{1}}{{m}_{2}}=2\times \left( -\frac{1}{2} \right)=-1\] \[\therefore \] The angle of intersection of the curves is \[\frac{\pi }{2}.\]


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