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  "body": "\n## Summary\n\nA plane algebraic curve is a curve in the affine or projective plane defined by one polynomial equation.\nIts degree is the degree of that polynomial.\nBy [[Bézout's theorem|KWNVF194D8]], it is the number of points in which a general line meets the curve.\nLines, conics and cubics are the plane curves of degree $1$, $2$ and $3$.\nMore generally, in geometry a plane curve is any curve that lies in a plane.\n\n## Explanations\n\n### L1 human\n\nA plane curve is the set of points $(x, y)$ satisfying one polynomial equation $f(x, y) = 0$.\nThe circle $x^2 + y^2 = 1$ has degree $2$, and the curve $y^2 = x^3 - x$ has degree $3$.\nAdding points at infinity gives a projective plane curve, defined by a homogeneous polynomial in three variables.\nMany properties of the curve, such as its [[genus|6W8TDV9VVN]] when it is smooth, can be read off from the degree alone.\n",
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