question_answer

The equation of the circle that can be inscribed in the square OABC, where O is the origin \[A(-2,0),\,B(-2,2)\] and \[C(0,2)\] is

A)   \[{{x}^{2}}+{{y}^{2}}+2x-2y=0\]

B)  \[{{x}^{2}}+{{y}^{2}}+2x-2y+1=0\]

C)  \[{{x}^{2}}+{{y}^{2}}+2x-2y-1=0\]

D)  \[{{x}^{2}}+{{y}^{2}}-2x+2y+1=0\]

Correct Answer: B

Solution :

By plotting, we get the centre of the circle,  which is inscribed in the square OABC is \[(-1,1)\] and radius is 1. \[\therefore \] Equation of circle is \[{{(x+1)}^{2}}+{{(y-1)}^{2}}={{1}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}+2x-2y+1=0\]