A) touch externally
B) do not intersect
C) touch internally
D) intersect at two points
E) are concentric
Correct Answer: D
Solution :
The centres and radii of given circles \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\]and \[{{x}^{2}}+{{y}^{2}}+4x+6y+4=0\]are \[{{C}_{2}}(2,3),{{C}_{2}}(-2,-3)\]and \[{{r}_{1}}=\sqrt{4+9+12}=5,\] \[{{r}_{2}}=\sqrt{4+9-4}=3\] Now, \[{{C}_{1}}{{C}_{2}}=\sqrt{{{(2+2)}^{2}}+{{(3+3)}^{2}}}=\sqrt{52}\] Here, \[{{C}_{1}}{{C}_{2}}<{{r}_{1}}+{{r}_{2}}\] Hence, given circles intersect at two points.
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