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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The focal distance of a point on the parabola \[{{y}^{2}}=16x\] whose ordinate is twice the abscissa, is

    A)            6     

    B)            8

    C)            10   

    D)            12

    Correct Answer: B

    Solution :

               Let point be \[(h,k)\]. But \[2h=k,\]then \[{{k}^{2}}=16h\]                    Þ \[4{{h}^{2}}=16h\]Þ \[h=0,\,h=4\]Þ \[k=0,\,k=8\]                    \[\] Points are (0,0), (4,8). Hence focal distances are respectively \[0+a=4,\]\[4+4=8\]. \[(\because \,a=4)\]


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