 Varieties The roots of any polynomial in \(x\) and \(y\) form a curve in the plane called a one-dimensional variety of degree that of the polynomial. Thus lines are of degree 1, being expressed as polynomials \(ax+by+c\), while circles centered on \((x', y')\) are of degree 2, being expressed as polynomials \((x-x')^2 +(y-y')^2 -r^2\). Some varieties may contain no points, for example \(x^2 +y^2 +1\), while others may contain one point, for example \(x^2 +y^2\) having the origin as its one root. In general however a two-dimensional variety will be a curve. Such a curve may cross itself, or have a cusp, or even separate into two or more components not connected to each other.