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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
    Which of the following is a point on the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+2x-3y+6=0\]and \[{{x}^{2}}+{{y}^{2}}+x-8y-13=0\] Karnataka CET 2003]

    A)            (1, -2)                                       

    B)            (1, 4)

    C)            (1, 2)                                         

    D)            (1, -4)

    Correct Answer: D

    Solution :

               Equation of circles is                             \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2x-3y+6=0\]                     ..... (i)                    \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}+x-8y-13=0\]                      ..... (ii)                    \[\therefore \] Equation of common chord is                    \[{{S}_{1}}-{{S}_{2}}=0\] \[\Rightarrow x+5y+19=0\]                     .....(iii)                    and out of the four given points only point (1, ?4) satisfies it.


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