关于“伴生圆锥曲线”的切线方程

On the Tangent Equations of the "Companion Taper Curve"

直线被圆锥曲线截得弦的中点问题,是解析几何的重点和难点.常规解法,演算冗繁,计算量大,本文从理论上揭示圆锥曲线弦的中点本质特性出发,对“伴生圆锥曲线”的切线方程和“伴生圆锥曲线”与弦长关系进行探究从而为解这一类题提供统一、清晰、简捷的解法.

The problems about the midpoints of the chords cut by the taper curve are the most critical and difficult in analytic geometry problems. Common solutions are full of complex mathematical calculations. This essay offers general, clear, simple and direct solutions to them by theoretically indicating the essential characteristics of the midpoints of the chords, and by studying the tangent equations of 'companion taper curve' and the relationship between 'the companion taper curve' and the length of chords.