A) \[x-y-5=0\]
B) \[x-y+5=0\]
C) \[x-y-5=0\]
D) \[x+y+5=0\]
Correct Answer: C
Solution :
Let \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}-6x-12y+37=0\] and \[{{S}_{2}}\equiv {{x}^{2}}+{{y}^{2}}-6y+7=0\] The equation of common tangent of the two circles is\[{{S}_{2}}-{{S}_{2}}=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-6x-12y+37\] \[-({{x}^{2}}+{{y}^{2}}-6y+7)=0\] \[\Rightarrow \] \[-6x+6y+30=0\] \[\Rightarrow \] \[x-y-5=0\]
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