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KVPY Sample Paper KVPY Stream-SX Model Paper-31

  • question_answer
    Let vertices of the triangle ABC is \[A(0,0),B(0,1)\] and \[C(x,y)\] and perimeter is 4 then the locus of C is-

    A) \[9{{x}^{2}}+8{{y}^{2}}+8y=16\]

    B) \[8{{x}^{2}}+9{{y}^{2}}+9y=16\]

    C) \[9{{x}^{2}}+8{{y}^{2}}-8y=16\]

    D) \[8{{x}^{2}}+9{{y}^{2}}-9x=16\]

    Correct Answer: C

    Solution :

    \[\sqrt{{{x}^{2}}+{{y}^{2}}}+\sqrt{{{x}^{2}}+{{(y-1)}^{2}}}=3\]\[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-2y+1=9+{{x}^{2}}+{{y}^{2}}-6\sqrt{{{x}^{2}}+{{y}^{2}}}\]
    \[3\sqrt{{{x}^{2}}+{{y}^{2}}}=4+y\]
    \[9{{x}^{2}}+9{{y}^{2}}=16+{{y}^{2}}+8y.\]


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