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

  • question_answer
    Let \[{{L}_{1}}\] be a straight line passing through the origin and \[{{L}_{2}}\] be the straight line \[x+y=1\]. If the intercepts made by the circle \[{{x}^{2}}+{{y}^{2}}-x+3y=0\] on \[{{L}_{1}}\] and \[{{L}_{2}}\] are equal, then which of the following equation can represent\[{{L}_{1}}\]?

    A) \[x+7y=0\]                 

    B) \[x-y=0\]

    C) \[x-7y=0\]                   

    D)  Both [a] and [b]

    Correct Answer: D

    Solution :

     Centre of the circle is\[\left( \frac{1}{2},\,\,-\frac{3}{2} \right)\]. Its distance from the line\[x+y-1\]is\[\sqrt{2}\]. Let the required line be\[mx-y=0\] \[\therefore \]    \[\left| \frac{\frac{m}{2}+\frac{3}{2}}{\sqrt{{{m}^{2}}+1}} \right|=\sqrt{2}\Rightarrow m=1,\,\,-17\] \[\therefore \]    The lines are\[x-y=0,\,\,x+7y=0\]


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