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本文对一道高考解析几何题的解法进行了探究,得出了一种简单的通解通法,并对其结论进行了推广与证明.题目(2014年高考北京卷文科数学试题)已知椭圆C:x~2+2y~2=4.(1)求椭圆C的离心率;(2)设O为原点,若点A在椭圆C上,点B在直线y=2上,且OA⊥OB,求直线AB与圆x~2+y~2=2的位置关系,并证明你的结论.
This paper explores a solution to the college entrance examination analytic geometry problem, has come up with a simple general solution method, and its conclusion has been popularized and proved. Subject (2014 college entrance examination Beijing liberal arts mathematics test) Known oval C: (2) Suppose O is the origin, if the point A is on the ellipse C, point B is on the line y = 2, and OA ⊥ OB, x 2 + 2y ~ 2 = Find the linear AB and the circle x ~ 2 + y ~ 2 = 2 position, and prove your conclusion.