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

  • question_answer
    A point moves in such a way that its distance from (1,-2) is always the twice from (-3,5), the locus of the point is  

    A) \[3{{x}^{2}}+{{y}^{2}}+26x+44y-131=0\]

    B) \[{{x}^{2}}+3{{y}^{2}}-26x+44y-131=0\]

    C) \[3({{x}^{2}}+{{y}^{2}})+26x-44y+131=0\]

    D) None of these

    Correct Answer: C

    Solution :

    \[{{(x-1)}^{2}}+{{(y+2)}^{2}}={{2}^{2}}[{{(x+3)}^{2}}+{{(y-5)}^{2}}]\] \[\Rightarrow \,\,3\,({{x}^{2}}+{{y}^{2}})+26x-44y+131=0\].


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