A) internally
B) externally
C) Do not say anything
D) None of these
Correct Answer: B
Solution :
The centre and radii of given circles are \[{{C}_{1}}(1,-3),{{C}_{2}}\left( \frac{5}{2},-3 \right)\]and \[{{r}_{1}}=\sqrt{1+9-6}=2\] \[{{r}_{2}}=\sqrt{\frac{25}{4}+9-15}=\sqrt{\frac{25-24}{4}}=\frac{1}{2}\] Now, \[{{C}_{1}}{{C}_{2}}=\sqrt{{{\left( 1-\frac{5}{2} \right)}^{2}}+{{(-3+3)}^{2}}}\] \[=\sqrt{{{\left( \frac{3}{2} \right)}^{2}}+0=\frac{3}{2}}\] and \[{{r}_{1}}-{{r}_{2}}=2-\frac{1}{2}=\frac{3}{2}\] \[\because \] \[{{r}_{1}}-{{r}_{2}}={{C}_{1}}{{C}_{2}}\] Hence, the two circle touch each other eternally.
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