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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2001

  • question_answer
    If the line\[x+2y=1\]is the polar of the circle \[{{x}^{2}}+{{y}^{2}}=5,\]then pole is

    A)  \[(5,10)\]            

    B)  \[(5,5)\]

    C)  \[(-5,10)\]           

    D)  \[(-5,-10)\]

    Correct Answer: A

    Solution :

     Let the pole be\[({{x}_{1}},{{y}_{1}}),\]then polar is \[x{{x}_{1}}+y{{y}_{1}}=5\]                  ...(i) But given polar is \[x+2y=1\]                ...(ii) On comparing Eqs.(i) and (ii), \[\frac{{{x}_{1}}}{1}=\frac{{{y}_{1}}}{2}=\frac{5}{1}\] \[\Rightarrow \] \[{{x}_{1}}=5,{{y}_{1}}=10\] Hence, pole is (5,10)


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