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1.试题呈现题1(2016年高考四川卷数学理科第20题)已知椭圆E:x~2/a~2+y~2/b~2=1(a>b>0)的两个焦点与短轴的一个端点是直角三角形的三个顶点,直线l:y=-x+3与椭圆E有且只有一个公共点T.(Ⅰ)求椭圆E的方程及点T的坐标;(Ⅱ)设O是坐标原点,直线l′平行于OT,与椭圆E交于不同的两点A,B,且与直线l交于点
1. Questions presented questions 1 (2016 Entrance Examination Sichuan Mathematics Mathematical Questions No. 20) Known elliptic E: x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0) of the two One endpoint of the focal point and the minor axis is the three vertices of the right triangle. The straight line l: y = -x + 3 and the ellipse E have only one common point T. (I) Find the equation of ellipse E and the coordinates of point T; ( Ⅱ) Suppose O is the origin of coordinates, the straight line l ’is parallel to OT, and the ellipse E intersects with two different points A, B, and intersects the straight line l