Curves | Analytic geometry

Circular algebraic curve

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, ifF = Fn + Fn−1 + ... + F1 + F0, where each Fi is homogeneous of degree i, then the curve F(x, y) = 0 is circular if and only if Fn 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. (Wikipedia).

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From playlist ⚡️Graph Linear Equations | Learn About

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Related pages

Circular points at infinity | Polynomial | Lemniscate of Bernoulli | Euclidean group | Watt's curve | Conchoid of de Sluze | Cassini oval | Inversive geometry | Geometry | Limaçon | Circle | Toric section | Cardioid | Complex projective plane | Homogeneous coordinates | Homogeneous function