JEE Main & Advanced Sample Paper JEE Main - Mock Test - 42

  • question_answer
    A straight line moves so that the sum of the reciprocals   of  its   intercepts   on   two perpendicular lines is constant, then the line passes through-

    A) A fixed point     

    B)        A variable point

    C) Origin   

    D)        None of these

    Correct Answer: A

    Solution :

    [a] Let line is \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{1}{a}+\frac{1}{b}=\lambda \Rightarrow \frac{1}{\lambda a}+\frac{1}{\lambda b}=1\] \[\frac{x}{a}+\frac{y}{b}=\frac{1}{\lambda a}+\frac{1}{\lambda b}\] \[\frac{1}{a}\left( x-\frac{1}{\lambda } \right)+\frac{1}{b}\left( y-\frac{1}{\lambda } \right)=0\] lines always passes through \[\left( \frac{1}{\lambda },\frac{1}{\lambda } \right)\]


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