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JEE Main & Advanced Sample Paper JEE Main Sample Paper-33

  • question_answer
    The locus of centroid of the triangle whose vertices are \[\left( acos\text{ }t,\text{ }asin\text{ }t \right),\] (b sin t, - bcos t) and (1,0) where t is a parameter, is

    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 :

    Let \[h=\frac{a\,\cos \,t+sin\,t\,+1}{3},\,k=\frac{a\,\sin \,t\,-\,b\,\cos \,t\,+0}{3}\] \[\Rightarrow \,{{(3h-1)}^{2}}+{{(3k)}^{2}}={{a}^{2}}+{{b}^{2}}\] \[\therefore \]Locus of \[\Rightarrow \,2{{x}_{2}}\,+{{y}_{2}}=0\] is \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]


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