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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation of the directrix of the parabola \[{{x}^{2}}+8y-2x=7\] is [UPSEAT 2004]

    A)            \[y=3\]                                      

    B)            \[y=-3\]

    C)            \[y=2\]                                      

    D)            \[y=0\]

    Correct Answer: A

    Solution :

               Given, equation of parabola is \[{{x}^{2}}+8y-2x=7\]\[\Rightarrow \]\[{{x}^{2}}-2x+8y-7=0\]                    \[\Rightarrow \]\[{{x}^{2}}-2x+1+8y-7-1=0\]\[\Rightarrow \] \[{{(x-1)}^{2}}+8y=8\]                    \[\Rightarrow \] \[{{(x-1)}^{2}}=-8(y-1)\]\[\Rightarrow \]\[{{(x-1)}^{2}}=-4.2(y-1)\]                    Here, \[a=2\].                    \[\therefore \] Equation of directrix is \[y-1=2\] i.e., \[y=3\].


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