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Question
ABCD is a square whose side is a; taking AB and AD as axes, prove that the equation of the circle circumscribing the square is x2 + y2 − a (x + y) = 0.
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Solution
Given:
ABCD is a square with side a units.
Let AB and AD represent the x-axis and the y-axis, respectively.
Thus, the coordinates of B and D are (a, 0) and (0, a), respectively.
The end points of the diameter of the circle circumscribing the square are B and D.
Thus, equation of the circle circumscribing the square is
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