A) \[{{x}^{2}}+{{y}^{2}}+ax+by=0\]
B) \[{{x}^{2}}+{{y}^{2}}-ax+by=0\]
C) \[{{x}^{2}}+{{y}^{2}}-ax-by=0\]
D) \[{{x}^{2}}+{{y}^{2}}+ax-by=0\]
Correct Answer: C
Solution :
Equation of circle passing through (0, 0) is \[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\] ?.(i) Also, circle (i) is passing through (0, b) and (a, b) \[\therefore \]\[f=-\frac{b}{2}\] and \[{{a}^{2}}+{{b}^{2}}+2ag+2\text{ }\left( -\frac{b}{2} \right)\text{ }b=0\] \[\Rightarrow g=-\frac{a}{2}\] Hence the equations of circle is, \[{{x}^{2}}+{{y}^{2}}-ax-by=0\].
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