题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-36368.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-29930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-45481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-66636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-66636.png)
解析
【错解分析】椭圆的定义、等差数列的定义,处理直线与圆锥曲线的方法
【正解】(1)由椭圆定义及条件知,2a=|F1B|+|F2B|=10,得a=5,又c=4,所以b=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-14044.png)
故椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-28942.png)
(2)由点B(4,yB)在椭圆上,得|F2B|=|yB|=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-49709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-74532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-23619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-23619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-74532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-23619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-74532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-23619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-74532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-23619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-74532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-49709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-44543.png)
(3)解法一 由A(x1,y1),C(x2,y2)在椭圆上 得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-42039.png)
①-②得9(x12-x22)+25(y12-y22)=0,即9×
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-13852.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-36651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-25704.png)
即k=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-34437.png)
所以m=y0-4k=y0-
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-57242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-69837.png)
得-
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-49709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-49709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-66636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011109-66636.png)
解法二 因为弦AC的中点为P(4,y0),所以直线AC的方程为
y-y0=-
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-25704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011110-28942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-71574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011111-34437.png)
核心考点
试题【如图,已知某椭圆的焦点是F1(-4,0)、F2(4,0),过点F2并垂直于x轴的直线与椭圆的一个交点为B,且|F1B|+|F2B|=10,椭圆上不同的两点A(x】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011055-49641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011056-46967.png)
(1)若正方形中心M为(2,2)时,求点N(b,c)的轨迹方程。
(2)求证方程
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011056-92159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011056-62922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011056-76899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011056-45504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011051-25489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011051-28206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011052-74652.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
已知椭圆C中心在原点,焦点在
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-27643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-76237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-54499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-80590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-27643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-47107.png)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-80590.png)
(2)求椭圆C长轴的取值范围。
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011028-13707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011028-58394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011028-56144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-40910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-22240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-93341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-79375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-64735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-16117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-13855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-65365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-96885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-13855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-97323.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-13855.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-87599.png)
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