A) \[{{x}^{2}}+{{y}^{2}}-4y-2y+5=0\]
B) \[{{x}^{2}}+{{y}^{2}}-4x-2y-5=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4x-2y-4=0\]
Correct Answer: C
Solution :
Distance from centre (2, 1) to the line \[3x+4y-5=\]; Radius- of circle \[\Rightarrow \] \[\frac{|3\,\,(2)+4\,(1)-5|}{\sqrt{{{3}^{2}}+{{4}^{2}}}}=r\] \[\Rightarrow \] \[\frac{5}{5}=r\,\,\,\Rightarrow \,\,\,\,r=1\] \[\therefore \] Equation of circle is \[{{(x-2)}^{2}}+{{(y-1)}^{2}}={{1}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-4x-2y+4+1=1\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\]
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