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11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer
    The line \[x-1=0\] is the directrix of the parabola \[{{y}^{2}}-kx+8=0\]. Then one of the values of k is  [IIT Screening 2000]

    A)            \[\frac{1}{8}\]                           

    B)            8

    C)            4     

    D)            \[\frac{1}{4}\]

    Correct Answer: C

    Solution :

               The parabola is \[{{y}^{2}}=4.\frac{k}{4}\left( x-\frac{8}{k} \right)\].                   Putting \[y=Y,\,x-\frac{8}{k}=X,\] the equation is \[{{Y}^{2}}=4.\,\frac{k}{4}.X.\]                   \ The directrix  is \[X+\frac{k}{4}=0,\]i.e. \[x-\frac{8}{k}+\frac{k}{4}=0\].                    But \[x-1=0\] is the directrix. So, \[\frac{8}{k}-\frac{k}{4}=1\] \[\Rightarrow \,k=-8,\,4.\]


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