The equation of a circle whose end points of a diameter are (x1, y1) and (x2, y2) is

1
(x – x1) (x – x2) +(y – y1) (y – y2) = x2 + y2
2
(x – x1)2 + (y – y1)2 = x2y2
3
x2 + y2 + 2x1x2 + 2y1y2 = 0
4
(x – x1) (x –x2) + (y – y1) (y – y2) = 0

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