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

  • question_answer
    Locus of centroid of the triangle whose vertices are \[(a\cos t,a\sin t),\ (b\sin t,-b\cos t)\] and (1, 0), where t is a parameter; is   [AIEEE 2003]

    A) \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]

    B) \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

    C) \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

    D) \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]

    Correct Answer: B

    Solution :

    \[3h=a\cos t+b\sin t+1,\,\,3k=a\sin t-b\cos t\] \[{{a}^{2}}+{{b}^{2}}={{(3h-1)}^{2}}+{{(3k)}^{2}}\] \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\].


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