JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The line \[y=mx+c\] touches the parabola \[{{x}^{2}}=4ay\], if  [MNR 1973; MP PET 1994, 99]

    A)            \[c=-am\]                                  

    B)            \[c=-a/m\]

    C)            \[c=-a{{m}^{2}}\]                      

    D)            \[c=a/{{m}^{2}}\]

    Correct Answer: C

    Solution :

               \[{{x}^{2}}=4a(mx+c)\]Þ \[{{x}^{2}}-4amx-4ac=0\]            It touches, then \[{{B}^{2}}-4AC=0\]            Þ \[16{{a}^{2}}{{m}^{2}}+16ac\]Þ\[\Rightarrow \]Þ\[c=-a{{m}^{2}}\].


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