JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Critical Thinking

  • question_answer
    The locus of the point \[P(x,y)\] satisfying the relation \[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}+\sqrt{{{(x+3)}^{2}}+{{(y-1)}^{2}}}=6\] is [Orissa JEE 2002]

    A)            Straight line                          

    B)            Pair of straight lines

    C)            Circle                                       

    D)            Ellipse

    Correct Answer: B

    Solution :

               \[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}+\sqrt{{{(x+3)}^{2}}+{{(y-1)}^{2}}}=6\]             \[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}=6-\sqrt{{{(x+3)}^{2}}+{{(y-1)}^{2}}}\]            Squaring both sides. We get,                                 \[12x+36=12\sqrt{{{(x+3)}^{2}}+{{(y-1)}^{2}}}\]            Again squaring we get the given equation is pair of straight lines.

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