JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 71) The circles \[{{x}^{2}}+{{y}^{2}}-2x-15=0\] and\[{{x}^{2}}+{{y}^{2}}+4y+3=0\]

    A)  no common tangent  

    B)  one common tangent

    C)  three common tangents

    D)  four common tangents.

    Correct Answer: A

    Solution :

    \[{{C}_{1}}(1,\,\,0);\,\,{{C}_{2}}(0,\,\,-2)\] \[{{r}_{1}}=\sqrt{1+15}=4;\,\,{{r}_{2}}=\sqrt{4-3}=1\] \[{{C}_{1}}{{C}_{2}}=\sqrt{1+4}=\sqrt{5}\] \[{{r}_{1}}-{{r}_{2}}=3\Rightarrow {{C}_{1}}{{C}_{2}}<{{r}_{1}}-{{r}_{2}}\] Hence, \[{{C}_{2}}\] lies inside\[{{C}_{1}}\].

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