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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-1

  • question_answer
    The equation of the directrix of the parabola \[{{\mathbf{y}}^{\mathbf{2}}}+\mathbf{4y}+\mathbf{4x}+\mathbf{2}=\mathbf{0}\]is

    A) \[2x=3\]                                   

    B) \[~x=3\]         

    C) \[3x=2\]                                   

    D) \[x=-3\]

    Correct Answer: A

    Solution :

    [a] Given equation of the parabola be \[{{y}^{2}}+4y+4x+2=0\] \[{{y}^{2}}+2.2y+4-4+4x+2=0\] \[{{(y+2)}^{2}}=-4\left( x-\frac{1}{2} \right)Let\,{{y}^{2}}=-4.x\] When \[{{y}^{2}}=-4a\text{ }X\] then equation of the directrix be \[X=a,here\text{ }a=1\text{ }and\text{ }X=x-\frac{1}{2}~\]        \[\therefore x-\frac{1}{2}~=1\] \[x=1+\frac{1}{2}=\frac{3}{2}\Rightarrow 2x=3\]


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