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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Chord of contact of tangent, Pole and Polar

  • question_answer
    The polar of the point (5, ?1/2) w.r.t  circle \[{{(x-2)}^{2}}+{{y}^{2}}=4\]is                                        [RPET 1996]

    A)            \[5x-10y+2=0\]                      

    B)            \[6x-y-20=0\]

    C)            \[10x-y-10=0\]                        

    D)            \[x-10y-2=0\]

    Correct Answer: B

    Solution :

               The polar of the point \[\left( 5,\ -\frac{1}{2} \right)\] is                    \[x{{x}_{1}}+y{{y}_{1}}+g(x+{{x}_{1}})+f(y+{{y}_{1}})+c=0\]                    \[\Rightarrow 5x-\frac{1}{2}y-2(x+5)+0+0=0\]                    \[\Rightarrow 3x-\frac{y}{2}-10=0\Rightarrow 6x-y-20=0\].


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