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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Transformation of axes and Locus

  • question_answer
    If the distance of any point P from the point \[A(a+b,a-b)\] and \[B(a-b,a+b)\]are equal, then the locus of P is   [Karnataka CET 2003]

    A) \[x-y=0\]

    B) \[ax+by=0\]

    C) \[bx-ay=0\]

    D) \[x+y=0\]

    Correct Answer: A

    Solution :

    Let coordinate of point P is (x, y) Given \[PA=PB\,\,\Rightarrow \,\,{{(PA)}^{2}}={{(PB)}^{2}}\] \[\Rightarrow \,\,{{\{x-(a+b)\}}^{2}}+{{\{y-(a-b)\}}^{2}}\] \[={{\{x-(a-b)\}}^{2}}+{{\{y-(a+b)\}}^{2}}\] \[\Rightarrow \,\,2x[-a-b+a-b]+2y[-a+b+a+b]=0\] \[\Rightarrow \,\,x\,(-2b)+y\text{ }(2b)=0\]\[\Rightarrow \,\,-x+y=0\,\,\Rightarrow \,\,x-y=0\].


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