Circular points at infinity

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In projective geometry, the circular points at infinity in the complex projective plane (also called cyclic points or isotropic points) are

(1: i: 0) and (1: −i: 0).

Here the coordinates are homogeneous coordinates (x: y: z); so that the line at infinity is defined by z = 0. These points are called circular points at infinity because they lie at infinity, on that line, and they also lie on all circles. In other words, both points satisfy the homogeneous equations of the type

Ax² + Ay² + 2B₁xz + 2B₂yz − Cz² = 0.

The case where the coefficients are all real gives the equation of a general circle (of the real projective plane).

The circular points at infinity are the points at infinity of the isotropic lines.

The cyclic points are invariant under translation and rotation.