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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
    Polar of origin (0, 0) with respect to the circle \[{{x}^{2}}+{{y}^{2}}+2\lambda x+2\mu y+c=0\] touches the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\], if  [RPET 1992]

    A)            \[c=r({{\lambda }^{2}}+{{\mu }^{2}})\]                         

    B)            \[r=c\,({{\lambda }^{2}}+{{\mu }^{2}})\]

    C)            \[{{c}^{2}}={{r}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\]   

    D)            \[{{r}^{2}}={{c}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\]

    Correct Answer: C

    Solution :

               Polar is\[\lambda x+\mu y+c=0\]. The condition of tangency \[p=r\]gives the result (c).


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