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11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer
    On the parabola \[y={{x}^{2}}\], the point least distance from the straight line \[y=2x-4\] is            [AMU 2001]

    A)            (1, 1)                                         

    B)            (1, 0)

    C)            (1, ?1)                                       

    D)            (0, 0)

    Correct Answer: A

    Solution :

               Given, parabola \[y={{x}^{2}}\]                                      .....(i)                       Straight line \[y=2x-4\]                                                .....(ii)            From (i) and (ii), \[{{x}^{2}}-2x+4=0\]            Let \[f(x)={{x}^{2}}-2x+4\], \ \[f'(x)=2x-2\].            For least distance, \[f'(x)=0\] \[\Rightarrow \,2x-2=0\] Þ \[x=1\]            From \[y={{x}^{2}}\], \[y=1\]            So the point least distant from the line is (1, 1).     


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