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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