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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        What is the number of common tangents to the circles\[{{x}^{2}}+{{y}^{2}}=1\]and\[{{x}^{2}}+{{y}^{2}}-4x+3=0\]?

    A)  One                                     

    B)  Two

    C)  Three    

    D)  Four

    Correct Answer: C

    Solution :

                    Centres and radii of circles are\[{{C}_{1}}(0,0),{{r}_{1}}=1\] and\[{{C}_{2}}(2,0),{{r}_{2}}=\sqrt{4-3}=1\] Now, \[{{C}_{1}}{{C}_{2}}=\sqrt{{{(2-0)}^{2}}+0}=2={{a}_{1}}+{{a}_{2}}\] Hence, two circles touch each other externally, so there are 3 common tangents are possible.                  


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