A) \[{{x}^{2}}+{{y}^{2}}+5x+5y+12=0\]
B) \[{{x}^{2}}+{{y}^{2}}-5x-5y+12=0\]
C) \[{{x}^{2}}+{{y}^{2}}+5x-5y+12=0\]
D) \[{{x}^{2}}+{{y}^{2}}-5x+5y-12=0\]
Correct Answer: B
Solution :
Let the points be \[A=(2,\,\,2)\] and \[B=(3,\,3)\] Since, the circle passing through these points, so they satisfie the equation of the circle. Now, taking option , Let \[S\equiv {{x}^{2}}+{{y}^{2}}-5x-5y+12=0\] At \[A=(2,2)\] \[{{2}^{2}}+{{2}^{2}}-5(2)-5(2)+12=0\] \[\Rightarrow \] \[0=0\] At \[B=(3,3)\] \[{{3}^{2}}+{{3}^{2}}-5(3)-5(3)+12=0\] \[\Rightarrow \] \[0=0\] Hence, option [b] is correct.
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