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笔者有幸参加了2013年安徽省高考数学阅卷工作,笔者批阅的是理科数学第18题,这是一道解析几何试题.本文就是笔者在阅卷过程中的一点感触,与同行们作个交流.1试题再现第18题设椭圆E:x2a2+y21-a2=1的焦点在x轴上.(1)若椭圆E的焦距为1,求椭圆E的方程;(2)设F1,F2分别是椭圆E的左、右焦点,P为椭圆E上第一象限内的点,直线F2P交y轴于点Q,并且F1P⊥F1Q.证明:当a变化时,点P在某定直线上.(如图1)(1)解略;
I was fortunate enough to participate in the 2013 college entrance examination in Anhui Province mathematics marking work, the author is approaching the subject of Mathematics 18, which is a analytic geometry test.This article is the author in the marking process a little touch, and colleagues to make a exchange.1 questions Reproduce the eighteenth problem Ellipse E: x2a2 + y21-a2 = 1 focus on the x-axis. (1) If the ellipse E focal length is 1, find the equation of the ellipse E; (2) Let F1 and F2 be the ellipse E , P is the point in the first quadrant of the ellipse E, and the straight line F2P intersects the y-axis at point Q and F1P⊥F1Q. Proof: when a changes, the point P is on a certain straight line 1) (1) Solution