多种角度探究椭圆的焦半径、焦点弦、∠F1PF2的最大值问题

The Maximum of Focal Radius, Chord of Focus and Angle ∠F1PF2 of Ellipse Are Studied from Different Angles

摘要: 椭圆的焦半径、焦点弦、焦点三角形等相关知识是高考的难点，也是学生最容易混淆的知识点之一，只有在学生掌握相关结论的基础上才能更好地解决相关习题。本文主要运用代数、参数方程等方法以及数形结合的思想探究了焦半径、焦点弦的最值问题及焦点三角形的角∠F1PF2最大值问题，从多个角度分析了相关问题，更有助于培养学生的发散思维能力。

Abstract: The focus radius, focus chord and focus triangle of ellipse are the difficult points in the college en-trance examination. Only on the basis of students’ mastery of the relevant conclusions can they better solve the relevant exercises. In this paper, the maximum of focal radius, the chord of focal point and the maximum of angle of focal triangle are studied by means of algebra, parametric equation and the thought of the combination of number and shape. It is more helpful to cultivate students’ ability of divergent thinking.