数列与解析几何互相渗透,内容就变得丰富多彩,方法也就更加灵活了. 例1 已知某椭圆的焦点是F1(-4,0),F2(4,0),过点F2且垂直于x轴的直线与椭圆的一个交点为B,|F1B|+|F2B|=10.椭圆上不同的两点A(x1,y1),C(x2,y2)满足条件:|F2A|,|F2B|,|F2C|成等差数列. (1)求该椭圆的方程; The series and analytic geometry infiltrate each other, the content becomes rich and colorful, and the method is more flexible. Example 1 It is known that the focus of an ellipse is F1(-4,0), F2(4,0), F2 and F2 An intersection point between the straight line and the ellipse on the x-axis is B, |F1B|+|F2B|=10. Two different points A(x1,y1) and C(x2,y2) on the ellipse satisfy the condition: |F2A|,| F2B|,|F2C| into arithmetic series. (1) Find the equation of the ellipse;