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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    The number of common tangents to the circles\[{{x}^{2}}+{{y}^{2}}=4\]and\[{{x}^{2}}+{{y}^{2}}-8x+12=0\]is:

    A)  1                                            

    B)  2                            

    C)  3                            

    D)         4

    E)  none of these

    Correct Answer: C

    Solution :

    The centre and radius of circle\[{{x}^{2}}+{{y}^{2}}=4\]are \[{{C}_{1}}(0,\text{ }0)\]and\[{{r}_{1}}=2\]respectively and the centre and radius of circle\[{{x}^{2}}+{{y}^{2}}-8x+12=0\]are \[(4,0)\]and\[{{r}_{2}}=2\]. \[\because \]     \[{{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}}\] \[\therefore \]Circles touch each other externally, therefore number of common tangents are 3.


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