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

  • question_answer
    Without changing the direction of coordinate axes, origin is transferred to \[(h,k)\], so that the linear (one degree) terms in the equation \[{{x}^{2}}+{{y}^{2}}-4x+6y-7\]=0 are eliminated. Then the point \[(h,k)\]is

    A) (3, 2)

    B) (- 3, 2)

    C) (2, - 3)

    D) None of these

    Correct Answer: C

    Solution :

    Putting \[x={x}'+h,\,\,y={y}'+k,\] the given equation transforms to  \[{{{x}'}^{2}}+{{{y}'}^{2}}+{x}'(2h-4)+{y}'(2k+6)+{{h}^{2}}+{{k}^{2}}-7=0\] To eliminate linear terms, we should have \[2h-4=0,\,\,2k+6=0\,\,\,\Rightarrow \,\,h=2,\,\,k=-3\] i.e., \[(h,\,\,k)=(2,\,\,-3)\].


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