Can be centred anywhere. The circle x^2 + y^2 = z^2 is centred at the origin. X, y & z do not require to be different.
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x² + y² = 1.
The unit circle is a circle with its center at the origin and a radius of ' 1 '.
Equation of the circle: (x+1)^2 +(y+3)^2 = 25
All complex number that can be represented by the coordinates of points on the unit circle, that is, the circle with its centre at the origin and a radius of 1 unit.
Believe it or not, there are lots of such points.