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JCECE Engineering JCECE Engineering Solved Paper-2005

  • question_answer
    If two circles of the same radius rand centres at \[(2,\,\,3)\] and \[(5,\,\,6)\] respectively cut orthogonally, then the value of \[r\] is:

    A) \[3\]                                     

    B) \[2\]

    C) \[1\]                                     

    D) \[5\]

    Correct Answer: A

    Solution :

    Key Idea: Two circles cut orthogonally, if\[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]. The equation of circles whose centres \[(2,\,\,3)\] and\[(5,\,\,6)\], and radius \[r\] are                                 \[{{(x-2)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] \[\Rightarrow \]               \[{{x}^{2}}+{{y}^{2}}-4x-6y-{{r}^{2}}+13=0\] and                        \[{{(x-5)}^{2}}+{{(y-6)}^{2}}={{r}^{2}}\] \[\Rightarrow \]     \[{{x}^{2}}+{{y}^{2}}-10x-12y-{{r}^{2}}+61=0\]


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