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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 to the line bisecting the join of (3, -4) and (5, 2) and having its intercepts on the x-axis and the y-axis in the ratio 2 : 1 is       [Karnataka CET 2005]

    A) \[x+y-3=0\]                             

    B) \[2x-y=9\]

    C) \[x+2y=2\]                      

    D) \[2x+y=7\]

    Correct Answer: C

    Solution :

               Given equation of line having it intercepts on the x- axis and y?axis in the ratio 2:1 i.e., 2a and a                    \ \[\frac{x}{2a}+\frac{y}{a}=1\Rightarrow x+2y=2a\]                            ..... (i)                    According to question,                    Line (i) also passes through midpoint of \[(3,-4)\] and (5,2) i.e., \[(4,-1)\].                    \ \[4+2(-1)=2a\Rightarrow a=1\]                    Hence the equation of required line is, \[x+2y=2\].


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