A) \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0,\ {{x}^{2}}+{{y}^{2}}-10x-10y+25=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0,\ {{x}^{2}}+{{y}^{2}}-10x-10y-25=0\]
C) \[{{x}^{2}}+{{y}^{2}}+2x+2y+1=0,\ {{x}^{2}}+{{y}^{2}}+10x+10y+25=0\]
D) None of these
Correct Answer: A
Solution :
Equation of circle touching both the axes will be \[{{x}^{2}}+{{y}^{2}}-2ax-2ay+{{a}^{2}}=0\] Also it passes through (1, 2), therefore \[a=5,\ 1\]. Hence the equations of circles are \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] and \[{{x}^{2}}+{{y}^{2}}-10x-10y+25=0\].
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