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JEE Main & Advanced Mathematics Straight Line Question Bank Slope of line, Equation of line in different forms

  • question_answer
    The equation of straight line passing through point of intersection of the straight lines \[3x-y+2=0\] and \[5x-2y+7=0\] and having infinite slope is [UPSEAT 2001]

    A)            \[x=2\]                                      

    B)            \[x+y=3\]

    C)            \[x=3\]                                      

    D)            \[x=4\]

    Correct Answer: C

    Solution :

               Required line should be,                    \[(3x-y+2)+\lambda (5x-2y+7)=0\]                             ?..(i)                    Þ  \[(3+5\lambda )x-(2\lambda +1)y+(2+7\lambda )=0\]                    Þ  \[y=\frac{3+5\lambda }{2\lambda +1}x+\frac{2+7\lambda }{2\lambda +1}\]                              ?..(ii)                    As the equation (ii), has infinite slope, \[2\lambda +1=0\]                    Þ \[\lambda =-1/2\] putting \[\lambda =-1/2\] in equation (i) we have \[(3x-y+2)+(-1/2)(5x-2y+7)=0\]Þ \[x=3\].


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