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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 37

  • question_answer
    A line passes through (2, 2) and makes a triangle of axes 9 square units with co-ordinate axis in 1st Quadrant, the sum of all possible slopes of line is-

    A) \[-5/2\] 

    B)        \[-2\]    

    C) \[-3/2\] 

    D)        \[-1\]

    Correct Answer: A

    Solution :

    [a] Let line is \[\frac{x}{a}+\frac{y}{b}=1\] \[\because \]it passes through (2, 2) \[\Rightarrow \frac{2}{a}+\frac{2}{b}=1\]                       ???.(i) \[\because \]Area of triangle \[=\frac{1}{2}\left| ab \right|\] \[9=\frac{1}{2}|ab|\Rightarrow ab=18\]              ??...(ii) Solving (i) & (ii) a = 6     and    a = 3 b=3                  b=6 slope of line is \[-\frac{b}{a}\] i.e. \[-2,-\frac{1}{2}\]


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