A) \[{{x}^{2}}+{{y}^{2}}-4x-4y+7=0\]
B) \[{{x}^{2}}+{{y}^{2}}+4x+4y+7=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x-4y-7=0\]
D) None of the above
Correct Answer: A
Solution :
Give line is \[(x-2)\cos \theta +(y-2)\sin \theta =1\] \[={{\cos }^{2}}\theta +{{\sin }^{2}}\theta \] On comparing we get, \[x-2\cos \theta \] ...(i) \[y-2=\sin \theta \] ...(ii) and On squaring and then adding Eqs. (i) and (ii), we get \[{{(x-2)}^{2}}+{{(y-2)}^{2}}={{\cos }^{2}}\theta +{{\sin }^{2}}\theta \] \[\Rightarrow \]\[{{(x-2)}^{2}}+{{(y-2)}^{2}}=1\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-4x-4y+7=0\]
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