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2013年全国高考数学山东卷理科第22题:椭圆C:x2/a2+y2/b2=1(a>b>0)的左、右焦点分别是F1,F2,离心率为~(1/2)3/2,过F1且垂直于x轴的直线被椭圆C截得的线段长为l.(Ⅰ)求椭圆C的方程;(Ⅱ)点P是椭圆C上除长轴端点外的任一点,连接PF1,PF2.设∠F1PF2的角平分线PM交C的长轴于点M(m,0),求m的取值范围;(Ⅲ)在(Ⅱ)的条件下,过点P作斜率为k的直线l,使得l与椭圆C有且只有一个公共点.设直线PF1,PF2的斜率分别为k1,k2,若k≠0,试证明1kk1+1kk2为定值,并求出这个定值.
Shandong University of Science and Technology Volume 2013 Question 22: The left and right focal points of elliptical C: x2 / a2 + y2 / b2 = 1 (a> b> 0) are F1 and F2, respectively. ) 3/2, F1 and the line perpendicular to the x-axis of the line segment length ellipse C is l (I) find the equation of the ellipse C; (Ⅱ) P is the point on the ellipse C In the case of (II), set the value of m in the range of (m), (m) and Make a straight line l with slope k such that l has only one common point with the ellipse C. Let the slopes of the straight lines PF1 and PF2 be k1 and k2 respectively. If k ≠ 0, test that 1kk1 + 1kk2 is constant and find This setting.