一、问题呈现题目如图1,设椭圆x~2/a~2+y~2=1(a>1) .(1)求直线y=kx+1被椭圆截得的线段长(用a、k表示);(2)若任意以A(0,1)为圆心的圆与椭圆至多有3个公共点,求椭圆离心率的取值范围.本题是笔者所在学校的一道考题,选自2016年高考数学浙江卷理科第19题.考后统计发现此题得分率非常低,尤其是第(2)问,绝大多数学生因此问涉及的字母多,运算量 First, the problem presented in Figure 1, set the ellipse x ~ 2 / a ~ 2 + y ~ 2 = 1 (a> 1). (1) Find the line y = kx +1 is elliptical section length , K); (2) if any A (0,1) as the center of the circle and the ellipse at most 3 common points, find the ellipticity of the range of values. This is the author’s school exam, selected from 2016 college mathematics Zhejiang Crimping Division Question 19. Post-test statistics found that the problem scores very low, especially the first (2) asked most of the students asked so many letters involved, the amount of computation