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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    If the line \[2x+y+k=0\] is normal to the parabola \[{{y}^{2}}=-8x\],  then the value of k will be       [RPET 1986, 97]

    A)            \[-16\]                                       

    B)            \[-8\]

    C)            \[-24\]                                       

    D)            24

    Correct Answer: D

    Solution :

               \[y=-2x-k\]is normal to \[{{y}^{2}}=-8x\]            or \[-k=-\{-4(-2)-2{{(-2)}^{3}}\}=-(8+16)\]Þ \[\Rightarrow \,\frac{5}{3}=\frac{5}{2}({{e}^{2}}-1)\].


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