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众所周知,过二次曲线Ax~2+Cy~2+Dx+Ey+F=0 (g)上一点P_1(x_1,y_1)的切线方程为Ax_1x+Cy_1y+D((x_1+x)/2)+E((y_1+y)/2)+F=0(h)。这是一个将切点(曲线上的点)的坐标x_1、y_1与切线上的点(曲线外的点)的坐标x、y联系起来的公式。当已知切点P_1的坐标P_1(x_1,y_1)时,将x、y看作变量,则(h)为过P_1的切线上点的坐标满足的方程,即过P_1的切线方程。当已知曲线外一点P的坐标P(x,y)时,将x_1、y_1看作变量,则(h)
It is well known that the tangent equation of the point P_1(x_1,y_1) on the overconic curve Ax~2+Cy~2+Dx+Ey+F=0 (g) is Ax_1x+Cy_1y+D((x_1+x)/2). +E((y_1+y)/2)+F=0(h). This is a formula that relates the coordinates x_1, y_1 of the tangent point (point on the curve) to the coordinates x, y of the point (outside the curve) on the tangent line. When the coordinate P_1 (x_1, y_1) of the cut point P_1 is known, x and y are regarded as variables, and (h) is an equation satisfying the coordinates of the point on the tangent of P_1, that is, the tangent equation of P_1. When we know the coordinate P(x,y) of the point P outside the curve, consider x_1 and y_1 as variables, then (h)