A) \[{{x}^{2}}+{{y}^{2}}-4y-6=0\]
B) \[{{x}^{2}}+{{y}^{2}}+4y-14=0\]
C) \[{{x}^{2}}+{{y}^{2}}+4y+14=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4y-14=0\]
Correct Answer: D
Solution :
In circle, \[{{x}^{2}}+{{y}^{2}}+14x+6y+2=0\] \[g=7,\ f=3,\ c=2\] Centre of circle\[(-g,\ -f)=(0,\ 2)\], (Given) For orthogonally intersection, \[2gg'+2ff'=c+c'\] \[0-12=2+c'\Rightarrow c'=-14\] Put the values, in equation\[{{x}^{2}}+{{y}^{2}}+2g'x+2f'x+c'=0\]. \[\Rightarrow {{x}^{2}}+{{y}^{2}}+0-4y-14=0\Rightarrow {{x}^{2}}+{{y}^{2}}-4y-14=0\].
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