Question

The equation of circle which touches the $ x- $ axis and $y$ - 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 $

Answer 1

Answer: (B)

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 $