JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Equations of circle, Geometrical problems regarding circle

  • question_answer
    The equation of circle whose diameter is the line joining the points (­?4, 3) and (12, ?1) is  [IIT 1971; RPET 1984, 87, 89; MP PET 1984; Roorkee 1969; AMU 1979]

    A)            \[{{x}^{2}}+{{y}^{2}}+8x+2y+51=0\]

    B)            \[{{x}^{2}}+{{y}^{2}}+8x-2y-51=0\]

    C)            \[{{x}^{2}}+{{y}^{2}}+8x+2y-51=0\]                          

    D)            \[{{x}^{2}}+{{y}^{2}}-8x-2y-51=0\]

    Correct Answer: D

    Solution :

               Required equation is                    \[(x-{{x}_{1}})(x-{{x}_{2}})+(y-{{y}_{1}})(y-{{y}_{2}})=0\]                    \[(x+4)(x-12)+(y-3)(y+1)=0\]                    \[{{x}^{2}}+{{y}^{2}}-8x-2y-51=0\].


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