A) \[{{x}^{2}}+{{y}^{2}}+2x-4y-4=0\]
B) \[{{x}^{2}}+{{y}^{2}}+4x-2y-4=0\]
C) \[{{x}^{2}}+{{y}^{2}}-3x-4y=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4x-2y=0\]
Correct Answer: B
Solution :
Required equation of the circle, \[({{x}^{2}}+{{y}^{2}}-2x-6y+6)+\lambda (3x+2y-5)=0\] This circle passing through points\[(-2,\ 4)\], therefore \[(4+16+4-24+6)+\lambda (-6+8-5)=0\], \[\therefore \ \lambda =2\] \[\therefore \ ({{x}^{2}}+{{y}^{2}}-2x-6y+6)+2(3x+2y-5)=0\] \[\Rightarrow {{x}^{2}}+{{y}^{2}}+4x-2y-4=0\].
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