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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    On the parabola\[y={{x}^{2}}\], the point least distant from the straight line \[y=2x-4\] is

    A) \[(1,\,\,1)\]                                        

    B) \[(1,\,\,0)\]

    C) \[(1,\,\,-1)\]                      

    D) \[(0,\,\,0)\]

    Correct Answer: A

    Solution :

    Given, parabola is\[y={{x}^{2}}\]                              ... (i) straight line is\[y=2x-4\]                               ... (ii) From Eqs. (i) and (ii), we get                 \[{{x}^{2}}-2x-4=0\] Let          \[f(x)={{x}^{2}}-2x-4\] \[\therefore \]  \[f'(x)=2x-2\] For least distance, put\[f'(x)=0\] \[\Rightarrow \]               \[2x-2=0\] \[\Rightarrow \]               \[x=1\] From Eq. (i),\[y=1\] Hence, the point least distant from the line is\[(1,\,\,1).\]


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