Circular algebraic curve

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In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a polynomial divisible by x² + y². More precisely, if F = F_n + F_n−1 + ... + F₁ + F₀, where each F_i is homogeneous of degree i, then the curve F(x, y) = 0 is circular if and only if F_n is divisible by x² + y².

Equivalently, if the curve is determined in homogeneous coordinates by G(x, y, z) = 0, where G is a homogeneous polynomial, then the curve is circular if and only if G(1, i, 0) = G(1, −i, 0) = 0. In other words, the curve is circular if it contains the circular points at infinity, (1, i, 0) and (1, −i, 0), when considered as a curve in the complex projective plane.