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

  • question_answer
    ABC is a triangle in which angle C is a right angle. If the coordinates of A and B be (?3, 4) and (3,?4) respectively, then the equation of the circumcircle of triangle ABC is

    A)            \[{{x}^{2}}+{{y}^{2}}-6x+8y=0\]                                  

    B)            \[{{x}^{2}}+{{y}^{2}}=25\]

    C)            \[{{x}^{2}}+{{y}^{2}}-3x+4y+5=0\]                            

    D)            None of these

    Correct Answer: B

    Solution :

               AB must be diameter because semi-circle subtends right angle to circumference. Therefore, find the equation of circle as the line joining the points \[A(-3,\ 4)\] and \[B(3,\ -4)\] as diameter.


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