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在解析几何学中,我们把二元二次方程在平面的仿射坐标系(包括直角坐标系作为其特别情形)里所代表的曲线叫做二阶曲线。通过用坐标变换把方程化简的方法,最后可以断定,二阶曲线按其形状来分共有九种,各种曲线的最简单的方程是: 1.椭圆(包括圆) x~2+y~2-1=0, 2.虚椭圆 x~2+y~2+1=0, 3.双曲线 x~2-y~2-1=0, 4.一对相交的直线 x~2-y~2=0, 5.一个点(点椭圆或者说是一对虚的相交直线) x~2+y~2=0, 6.抛物线 x~2-y=0,
In analytical geometry, we refer to the curve represented by the binary quadratic equation in the plane’s affine coordinate system (including the Cartesian coordinate system as its special case) as a second-order curve. By using the coordinate transformation to simplify the equation, we can conclude that the second-order curve is divided into nine types according to its shape. The simplest equations for various curves are: 1. Ellipse (including circles) x~2+y~ 2-1=0, 2. Imaginary ellipses x~2+y~2+1=0, 3. Hyperbola x~2-y~2-1=0, 4. A pair of intersecting straight lines x~2-y ~2=0, 5. A point (point ellipse or a pair of virtual intersecting lines) x~2+y~2=0, 6. Parabola x~2-y=0,