2010年北京东城1月份高三检测卷的一道题为:已知椭圆C的中心在原点,一个焦点F(0,2),且长轴长与短轴长的比是2.(Ⅰ)求椭圆C的方程;(Ⅱ)若椭圆C在第一象限的一点P的横坐标为1,过点P作倾斜角互补的两条不同的直线PA,PB分别交椭圆C于另外两点A,B,求证:直线AB的斜率为定值; 2010 Beijing Dongcheng high school sentry in January to test the volume of a question: known center of the ellipse C at the origin, a focal point F (0,2), and the ratio of major axis length to minor axis length is 2. (Ⅰ) Find the ellipse (2) If the abscissa of a point P of ellipse C in the first quadrant is 1, then two different straight lines PA and PB, which are complementary to each other with an oblique angle, pass through the ellipse C at the other two points A and B , Verify: the slope of a straight line AB as a fixed value;