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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{y}^{2}}-6x-8y+24=0\] is

    A)  3                                            

    B)         4                            

    C)         2                                            

    D)         1

    Correct Answer: B

    Solution :

    The centres and radii of circles are \[{{C}_{1}}(0,0),{{C}_{2}}(3,4)\] and \[{{r}_{1}}=2,{{r}_{2}}=\sqrt{9+16-24}=1\] Now,     \[{{C}_{1}}{{C}_{2}}=\sqrt{{{(3-0)}^{2}}+{{(4-0)}^{2}}}=5\]                 \[{{r}_{1}}+{{r}_{2}}=2+1=3\] Since, \[{{C}_{1}}{{C}_{2}}>{{r}_{1}}+{{r}_{2}}\] \[\therefore \]  Number of common tangents = 4.


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