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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The focus of the parabola \[{{x}^{2}}=2x+2y\] is

    A)            \[\left( \frac{3}{2},\ \frac{-1}{2} \right)\]                                   

    B)            \[\left( 1,\ \frac{-1}{2} \right)\]

    C)            (1, 0)                                         

    D)            (0, 1)

    Correct Answer: C

    Solution :

               The parabola is \[{{x}^{2}}-2x=2y\]            or \[{{x}^{2}}-2x+1=2y+1\]Þ \[{{(x-1)}^{2}}=2\left( y+\frac{1}{2} \right)\]            Here \[4a=2\Rightarrow a=\frac{1}{2}\]            Now focus is \[\left( x-1=0,\,y+\frac{1}{2}=\frac{1}{2} \right)\,\,i.e.,\,(1,\,0)\].


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