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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The line \[x-y+2=0\] touches the parabola \[{{y}^{2}}=8x\] at the point              [Roorkee 1998]

    A)            \[(2,\ -4)\]                                

    B)            \[(1,\ 2\sqrt{2})\]

    C)            \[(4,\ -4\sqrt{2})\]                    

    D)            (2, 4)

    Correct Answer: D

    Solution :

               Intersection of \[x-y+2=0\] with \[{{y}^{2}}=8x\] is given by \[{{(x+2)}^{2}}=8x\]Þ\[{{x}^{2}}+4-4x=0\] Þ\[{{(x-2)}^{2}}=0\]                    \[\therefore x=2\]and\[y=x+2=4\].


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