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In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a polynomial divisible by x + y. More precisely, ifF = Fn + Fn−1 + ... + F1 + F0, where each Fi is homogeneous of degree i, then the curve F = 0 is circular if and only if Fn is divisible by x + y.
Equivalently, if the curve is determined in homogeneous coordinates by G = 0, where G is a homogeneous polynomial, then the curve is circular if and only if G = G = 0. In other words, the curve is circular if it contains the circular points at infinity, and , when considered as a curve in the complex projective plane.
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