A) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
B) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]
C) \[2{{x}^{2}}+{{y}^{2}}-2x-y=0\]
D) \[{{x}^{2}}+2{{y}^{2}}-x-2y=0\]
Correct Answer: A
Solution :
The standard equation of circle\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0,\] equation of the circle passing through (1, 0) is \[1+2g+c=0...(i)\]equation of the circle passing through (0, 1) is\[1+2f+c=0...(ii)\] since both the circles pass through the origin (0, 0) therefore\[c=0...(iii)\] equation (i), (ii) and \[(iii),g=-1/2,\]\[f=-1/2,c=0\] \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
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