论文部分内容阅读
已知椭圆x~2/9+y~2/4=1和点D(0,3),点M、N在椭圆上,且DM=λDN,求λ的取值范围。学生解得λ∈[1/5,5],并发现当点M、N分别与椭圆短轴两端点重合时,λ取最值。这仅仅是个巧合吗?以此为契机,对y轴上的动点到椭圆上的点的最远距离和最近距离展开了一次研究性学习,探究得到下面的结论。结论1:设Q是椭圆x~2/a~2+y~2/b~2=1(a>b>0)上的动点,点D(0,y_0)是.y轴正半轴上的一点,则有:
Known ellipse x ~ 2/9 + y ~ 2/4 = 1 and D (0,3), the point M, N on the ellipse, and DM = λDN, find the range of λ. Students solve λ ∈ [1 / 5,5], and find that when points M and N coincide with the two ends of elliptical minor axis respectively, λ takes the most value. Is this just a coincidence? Taking this as an opportunity, we conducted a research study on the farthest distance and the nearest distance to the point on the y-axis from the moving point to the ellipse. The following conclusions are drawn. Conclusion 1: Let Q be a moving point on the elliptic x2 / a2 + y2 / b2 = 1 (a> b> 0) On the point, there are: