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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    If \[x+y=k\] is a normal to the parabola \[{{y}^{2}}=12x\], then k is [IIT Screening 2000]

    A)            3     

    B)            9

    C)            ?9   

    D)            ?3

    Correct Answer: B

    Solution :

               Any normal is \[y+tx=6t+3{{t}^{3}}.\] It is identical with \[x+y=k\] if  \[\frac{t}{1}=\frac{1}{1}=\frac{6t+3{{t}^{3}}}{k}\]                    \[\therefore \]\[t=1\] and \[(a,\,\,\pm \,2a).\] Þ \[k=9.\]


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