A) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]
B) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
C) \[{{x}^{2}}+{{y}^{2}}+x-y=0\]
D) \[{{x}^{2}}+{{y}^{2}}-x+y=0\]
Correct Answer: B
Solution :
Given, equation of line is \[y=x\] ?.(i) and equation of a circle is \[{{x}^{2}}+{{y}^{2}}-2x=0\] ?(ii) on putting the value of y from Eq. (i) in Eq. (ii), we get \[{{x}^{2}}+{{x}^{2}}-2x=0\] \[\Rightarrow \] \[2x(x-1)=0\] \[\Rightarrow \] \[x=0,1\] Then from Eq. (i), we get \[y=0,1\] Let \[A=(0,0)\] and \[B=(1,1)\] Now, equation of circle o AB as a diameter is \[(x-0)(x-1)+(y-0)(y-1)=0\] \[\Rightarrow \] \[x(x-1)+y(y-1)=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
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