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JCECE Engineering JCECE Engineering Solved Paper-2010

  • question_answer
    If \[2x+y+k=0\]is a normal to the parabola\[{{y}^{2}}=-8x\], then the value of \[k\] is

    A) \[-16\]                                 

    B) \[-8\]

    C) \[-24\]                                 

    D) \[24\]

    Correct Answer: D

    Solution :

    We know that, the equation of normal to the parabola                 \[{{y}^{2}}=4ax\]is                   \[y=mx-2am-a{{m}^{3}}\] Equation of normal to the parabola \[{{y}^{2}}=-8x\] is                 \[y=mx+4m+2{{m}^{3}}\]                            ? (i) \[(\because \,\,a=2)\] But given normal is                 \[2x+y+k=0\]                                     ... (ii) Comparing Eqs. (i) and (ii), we get                 \[m=-2\]and\[k=-4m-2{{m}^{3}}\] \[\Rightarrow \]               \[k=8+16\] \[\Rightarrow \]               \[k=24\]


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