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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    \[{{x}^{2}}+{{y}^{2}}-16x-20y+164={{r}^{2}}\] and \[{{(x-4)}^{2}}+(y-{{7}^{2}})=36\] intersect at two distinct points, then:

    A) \[0<r<1\]

    B) \[1<r<11\]

    C) \[r>11\]

    D) \[r=11\]

    Correct Answer: B

    Solution :

    \[{{x}^{2}}+{{y}^{2}}-16x-20y+164={{r}^{2}}\]
    A (8, 10),           \[{{R}_{1}}=r\]
    \[{{(x-4)}^{2}}+{{(y-7)}^{2}}=36\]
    B (4, 7),            \[{{R}_{2}}=6\]
    \[\left| {{R}_{1}}-{{R}_{2}} \right|\,<\,AB\,<\,{{R}_{1}}+{{R}_{2}}\]
    \[\Rightarrow \]   \[1<r<11.\]


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