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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 17

  • question_answer
    A line with positive rational slope, passes through the point \[M\,(6,0)\] and is at a distance of 5 units from\[N\,(1,3)\]. The slope of line equals

    A) \[\frac{15}{8}\]                     

    B)        \[\frac{8}{15}\]         

    C) \[\frac{5}{8}\]                      

    D)        \[\frac{8}{5}\]

    Correct Answer: B

    Solution :

          [b] Let the required line be \[(y-0)=m\,(x-6),\,\,m>0\] or \[mx-y-6m=0\]                     ...(1) As distance of above line from \[N(1,3)\] is 5, we have \[\left| \frac{m-3-6m}{\sqrt{1+{{m}^{2}}}} \right|=5\Rightarrow {{(3+5m)}^{2}}=25(1+{{m}^{2}})\] \[\Rightarrow \,\,\,9+30m=25\Rightarrow m=16/30=8/15\]    


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