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求椭圆顶点弦的长度,通常用两点间距离公式求解,其过程不仅演算繁琐且过程冗长.本文介绍求椭圆顶点弦长度的一个公式,现说明如下.公式是否有其可行性和实用性,恳请同行赐教.引理经过椭圆(x~2/a~2)+(y~2/b~2)=1(a>b>0)长轴端点 A 的弦 AQ 交 y 轴于 R,过椭圆中心O的半弦 OP∥AQ,则|AQ|·|AR|=2|OP|~2.证明如图,设
Finding the length of the elliptic vertex is usually solved by the distance formula between two points. The process is not only complicated and complicated. This article introduces a formula for finding the length of the vertex of the ellipse, which is illustrated as follows. Whether the formula has its feasibility and practicality, Please enlighten colleagues. Lemma passes through the elliptic (x~2/a~2)+(y~2/b~2)=1(a>b>0) long-axis chord AQ intersection y-axis to R. The semi-chord OP∥AQ of the center O of the ellipse, then |AQ|·|AR|=2|OP|~2.