JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The co-ordinates of the extremities of the latus rectum of the parabola \[5{{y}^{2}}=4x\] are

    A)            \[(1/5,\ 2/5),\ (-1/5,\ 2/5)\]    

    B)            \[(1/5,\ 2/5),\ (1/5,\ -2/5)\]

    C)            \[(1/5,\ 4/5),\ (1/5,\ -4/5)\]    

    D)            None of these

    Correct Answer: B

    Solution :

               \[{{y}^{2}}=4.\frac{1}{5}x;\,\,a=\frac{1}{5}\]. Focus is \[\left( \frac{1}{5},0 \right)\] and co-ordinates of latus rectum are \[{{y}^{2}}=\frac{4}{25}\] Þ \[y=\pm \frac{2}{5}\]            or end points of latus rectum are \[\left( \frac{1}{5},\pm \frac{2}{5} \right)\]. 


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