J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer Suppose the straight line \[x+y=5\]touches the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]. Then, the coordinates of the point of contact are

    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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