question_answer

The equation of circle with centre (1, 2) and tangent \[x+y-5=0\]is                                               [MP PET 2001]

A)            \[{{x}^{2}}+{{y}^{2}}+2x-4y+6=0\]

B)            \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]

C)            \[{{x}^{2}}+{{y}^{2}}-2x+4y+8=0\]                            

D)            \[{{x}^{2}}+{{y}^{2}}-2x-4y+8=0\]

Correct Answer: B

Solution :

           \[\because \] Radius of circle = perpendicular distance of tangent from the centre of circle                                  \[\Rightarrow \]  \[r=\frac{1+2-5}{\sqrt{1+1}}=\sqrt{2}\]                    Hence the equation of required circle is                    \[{{(x-1)}^{2}}+{{(y-2)}^{2}}={{(\sqrt{2})}^{2}}\]                    \[\Rightarrow \,{{x}^{2}}+{{y}^{2}}-2x-4y+3=0.\]