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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 line passing through the point of intersection of the lines \[4x-3y-1=0\]and \[5x-2y-3=0\] and parallel to the line \[2y-3x+2=0,\] is                                                            [RPET 1985, 86, 88]

    A)            \[x-3y=1\]                                

    B)            \[3x-2y=1\]                              

    C)            \[2x-3y=1\]                              

    D)            \[2x-y=1\]

    Correct Answer: B

    Solution :

               The point of intersection of the lines is (1, 1). The equation of line parallel to \[2y-3x+2=0\] is \[2y-3x+k=0\]. It also passes through (1, 1), therefore\[AC=\sqrt{{{(4-0)}^{2}}+{{\left( 0-\frac{4}{3} \right)}^{2}}}=\frac{4\sqrt{10}}{3}\]. Hence the required equation is \[2y-3x+1=0\] or \[3x-2y=1\].


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