好的解析几何试题往往解法灵活,背景深刻,颇具研究价值,给人以美的享受.武汉市2017届高三二月调考解析几何试题便是其中一例.题目已知椭圆Γ:x~2/a~2+y~2/b~2=1(a>b>0)的左右焦点分别为F_1、F_2,离心率为2~(1/2)/2,F_2与椭圆上点的连线中最短的距离为2~(1/2)-1.(1)求椭圆的标准方程;(2)已知Γ上存在一点P,使得直线PF_1,PF_2 Good analytic geometry test often flexible solution, the background is profound, quite research value, give people the enjoyment of the United States.Wuhan City, the 2017 senior high school entrance exam analytic geometry test questions is one of them. Title Known oval Γ: x ~ 2 / The left and right focal points of a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0) are F_1 and F_2, respectively. The eccentricity is 2 1/2 (1/2) The shortest distance is 2 ~ (1/2) -1. (1) Find the standard equation of ellipse; (2) Knowing that there exists a point P on Γ such that the straight line PF_1, PF_2