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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

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

    A)  3                                            

    B)  2

    C)  1                            

    D)         5

    E)  6

    Correct Answer: A

    Solution :

    The equation of circles are \[{{(x-2)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-4x-6y-{{r}^{2}}+13=0\]           ...(i) and \[{{(x-5)}^{2}}+{{(y-6)}^{2}}={{r}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-10x-12y-{{r}^{2}}+61=0\]   ...(ii) The given circles cut orthogonally, if \[2.(-2)(-5)+2(-3)(-6)=\]                                 \[-{{r}^{2}}+13-{{r}^{2}}+61\] \[\Rightarrow \]\[20+36-13-61=-2{{r}^{2}}\] \[\Rightarrow \]               \[r=3\]


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