A) \[{{x}^{2}}+{{y}^{2}}+2x-4y-20=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\]
C) \[{{x}^{2}}+{{y}^{2}}+2x+4y-20=0\]
D) \[{{x}^{2}}+{{y}^{2}}-2x-2y-20=0\]
Correct Answer: B
Solution :
[b] Equation of circle be \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] Centre of the circle \[\equiv \left( 1,2 \right)\equiv \left( -g,-f \right)\] \[\therefore {{x}^{2}}+{{y}^{2}}-2x-4y+c=0\] ??.(1) This circle (1), passes through the point \[\left( 4,6 \right)\] Then \[{{\left( 4 \right)}^{2}}+{{6}^{2}}+2\times 4+4\times 6+c=0\] \[16+36-8-24+c=0\] \[52-32+c=0\] \[c=-20\] Hence, equation of the circle be \[{{x}^{2}}-{{y}^{2}}-2x-4y+20=0\] i.e. option [b] is correct.
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