离心率作为描述圆锥曲线的重要参量,在解析几何中尤显重要,在历年的高考中几乎每年都出现.求离心率的范围就必须建立不等关系,通过什么途径呢?本文就几种常规求法通过例题展现给读者. 例1 已知F1,F2是椭圆的两个焦点,点P在椭圆上,且∠F1PF2=60°,求椭圆离心率的取值范围. 解法1:设∠PF1F2=a,∠PF2F1=β,椭 Eccentricity is used as an important parameter to describe the conic section. It is particularly important in analytic geometry. It appears almost every year in the college entrance examinations over the years. The range of eccentricity must be established and the relationship must be established. What are the approaches? The method is presented to the reader through examples. Example 1 It is known that F1 and F2 are the two focal points of the ellipse, point P is on the ellipse, and ∠F1PF2=60°. Find the range of eccentricity of the ellipse. Solution 1: Set ∠PF1F2= a, ∠PF2F1=β, Ellipse