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

  • question_answer
    For what values of a and b the intercepts cut off on the coordinate axes by the line \[ax+by+8=0\] are equal in length but opposite in signs to those cut off by the line \[2x-3y+6=0\] on the axes                 [MP PET 1983]  

    A)            \[a=\frac{8}{3},\ b=-\ 4\]      

    B)            \[a=-\frac{8}{3},\ b=-\ 4\]

    C)            \[a=\frac{8}{3},\ b=4\]         

    D)            \[a=-\frac{8}{3},\ b=4\]

    Correct Answer: D

    Solution :

               The equation of lines in intercept form are \[\frac{x}{-8/a}+\frac{y}{-8/b}=1\]                               .....(i)                              \[\frac{x}{-3}+\frac{y}{2}=1\]                             ..... (ii)                    According to the condition, \[-\frac{8}{a}=-(-3)\]                    \[\Rightarrow a=-\frac{8}{3}\]and \[-\frac{8}{b}=-(2)\Rightarrow b=4\].


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