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

  • question_answer
    A square is inscribed in the circle\[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\], whose sides are parallel to the coordinate axes. One vertex of the square is   [IIT 1980; DCE 2001]

    A)            \[(1+\sqrt{2},\ -2)\]                 

    B)            \[(1-\sqrt{2},\ -2)\]

    C)            \[(1,\ -2+\sqrt{2})\]                 

    D)            None of these

    Correct Answer: D

    Solution :

                 Trick: Obviously the centre of the given circle is\[(1,-2)\]. Since the sides of square are parallel to the axes, therefore, first three alternates cannot be vertices of square because in first two (a and b) \[y=-2\] and in (c)\[x=1\], which passes through centre \[(1,\ -2)\] but it is not possible. Hence answer (d) is correct.


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