JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The focus of the parabola \[{{y}^{2}}-x-2y+2=0\]is         [UPSEAT 2000]

    A)            \[(1/4,\ 0)\]                              

    B)            (1, 2)

    C)            (3/4, 1)                                      

    D)            (5/4,1)

    Correct Answer: D

    Solution :

               Equation of parabola                     \[{{y}^{2}}-2y-x+2=0\]Þ \[{{(y-1)}^{2}}=(x-1)\]                    Let       \[y-1=Y\] and \[x-1=X\]                    \[{{Y}^{2}}=X,\,a=1/4\], focus \[=(1/4,\,0)\]                    \ Required focus = \[\left( \frac{1}{4}+1,\,0+1 \right)=(5/4,\,1)\].


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