JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The line \[lx+my+n=0\] will touch the parabola \[{{y}^{2}}=4ax\], if [RPET 1988; MNR 1977; MP PET 2003]

    A)            \[mn=a{{l}^{2}}\]                      

    B)            \[lm=a{{n}^{2}}\]

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

    D)            \[mn=al\]

    Correct Answer: C

    Solution :

               \[y=-\frac{l}{m}x-\frac{n}{m}\]            Condition for above line to be tangent to \[{{y}^{2}}=4ax\] is \[-\frac{n}{m}=\frac{am}{-l}\]or \[nl=a{{m}^{2}}\].


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