A) 47
B) \[-47\]
C) 49
D) \[-\text{ }49\]
Correct Answer: A
Solution :
Given two circles \[{{x}^{2}}+{{y}^{2}}-2x+22y+5=0\] \[{{x}^{2}}+{{y}^{2}}+14x+6y+k=0\] The two circles cut orthogonally, if \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})={{c}_{1}}+{{c}_{2}}\]i.e., \[2(-1.7+11.3)=5+k\] \[2(-7+33)=5+k\Rightarrow 52-5=k\Rightarrow k=47\].
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