JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation of normal to the parabola at the point \[\left( \frac{a}{{{m}^{2}}},\ \frac{2a}{m} \right)\],is     [RPET 1987]

    A)            \[y={{m}^{2}}x-2mx-a{{m}^{3}}\]    

    B)            \[{{m}^{3}}y={{m}^{2}}x-2a{{m}^{2}}-a\]

    C)            \[{{m}^{3}}y=2a{{m}^{2}}-{{m}^{2}}x+a\]                                   

    D)            None of these

    Correct Answer: C

    Solution :

               \[y-\frac{2a}{m}=-\frac{2a/m}{2a}\left( x-\frac{a}{{{m}^{2}}} \right)\]                    Þ \[y-\frac{2a}{m}=\frac{-1}{m}\left( x-\frac{a}{{{m}^{2}}} \right)\]                    Þ \[{{m}^{3}}y+{{m}^{2}}x-2a{{m}^{2}}-a=0\].


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