切线方程X_0X/a~2+Y_0Y/b~2=1的形式推广

• 作 者: 周焕鸿
• 机 构: 金华供销学校,
• 出 处: 中学教研
• 发表日期: 1991年01期
• 关键词: 切线方程 标准方程 平面直角坐标系 面上高 曲线方程 对应项 偏导 常数项 和式 中所

平面上的椭圆、双曲线、抛物线的标准方程为x~2/a~2±y~2/b~2=1、y~2=2px。在其曲线上的点(x_0,y_0)处的切线方程可表示为x_0x/a~2±y_0y/b~2=1、y_0y=p(x+x_0)的形式。这种形式与原曲线方程有明显的对应关系,便于记忆,并可以推广到平面上高次曲线。为了便于讨论,我们把平面直角坐标系中3次曲线方程的一般形式表示为

The standard equations for elliptic, hyperbolic and parabolic curves on the plane are x~2/a~2±y~2/b~2=1 and y~2=2px. The tangent equation at the point (x_0, y_0) on its curve can be expressed in the form of x_0x/a~2±y_0y/b~2=1, y_0y=p(x+x_0). There is a clear correspondence between this form and the original curve equation, which is easy to remember and can be extended to higher-order curves on the plane. For the sake of discussion, we denote the general form of the cubic curve equation in the plane rectangular coordinate system as