question_answer

The equation of circle which touches the\[x-\]axis and 7-axis at points (1, 0) and (0, 1) respectively, is

A)  \[{{x}^{2}}+{{y}^{2}}-4y+3=0\]

B)  \[{{x}^{2}}+{{y}^{2}}-2y-2=0\]

C)  \[{{x}^{2}}+{{y}^{2}}-2x-27+2=0\]

D)  \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\]

Correct Answer: B

Solution :

 Since, circle touches the x-axis and y-axis at points (1,0) and (0,1) respectively. So, centre of circle is (1,1) and radius is 1. Hence, equation of circle is \[{{(x-1)}^{2}}+{{(y-1)}^{2}}={{1}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\]