A) \[(3,2)\]
B) \[(2,3)\]
C) \[(4,1)\]
D) \[(1,4)\]
Correct Answer: B
Solution :
Given equation of circle, \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\] ?.(i) and equation of straight line, \[x+y=5\] ?.(ii) On solving Eqs. (i) and (ii), we get \[{{x}^{2}}+{{(5-x)}^{2}}-2x-4(5-x)+3=0\] \[\Rightarrow \] \[2{{x}^{2}}-8x+8=0\] \[\Rightarrow \] \[{{x}^{2}}-4x+4=0\] \[\Rightarrow \] \[{{(x-2)}^{2}}=0\] \[\Rightarrow \] \[x=2\] From Eq. (ii), \[y=3\] So, the point of contact is \[(2,3)\].
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