题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202243-48920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202243-89005.gif)
(1)求椭圆的离心率e
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202243-57734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202244-68891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202244-58031.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-89701.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-23995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-95743.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-15778.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202246-21430.gif)
∵OP∥AB,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202246-21264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202247-87389.gif)
解得:b=c.∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202247-41250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-23995.gif)
(2)由(1)知椭圆方程可化简为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202248-28548.gif)
易求直线QR的斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202248-62437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202304-26609.gif)
由①②消去y得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202304-33545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202304-60042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202304-81408.gif)
于是△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202244-58031.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202310-63414.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202310-28320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202310-32439.gif)
因此椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202311-53793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-95743.gif)
核心考点
试题【(本题满分12分)如图,过椭圆的左焦点作x轴的垂线交椭圆于点P,点A和点B分别为椭圆的右顶点和上顶点,OP∥AB.(1)求椭圆的离心率e(2)过右焦点作一条弦Q】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202229-47702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202229-87767.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202229-96039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-43607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-90349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-33521.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-90349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-99579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202216-30497.gif)
(1)若椭圆C上的点A(1,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202216-10604.gif)
(2)设点P是(1)中所得椭圆上的动点,当P在何位置时,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202216-39926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202208-42247.gif)
(1)求椭圆的离心率;
(2)若平行四边形OCED的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202208-59944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202208-16881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202200-58333.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-94782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-30494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-50402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-17359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202202-98253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202145-41250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202145-14998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202146-45902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202146-89458.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202146-37941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202146-35987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202146-72474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202147-65750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202147-18127.gif)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202147-85323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202147-22139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202148-85524.gif)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202147-65750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202147-85323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202148-35880.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202148-89777.gif)
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