题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180236-88647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180236-31778.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180236-93064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-67657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-54776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-27150.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-19402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-56715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-11996.gif)
(Ⅰ)求椭圆的方程;
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-67978.gif)
(Ⅲ)试用
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-67978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-69803.gif)
答案
解:(Ⅰ)依题意可得,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-90190.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-60139.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-51524.gif)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-34154.gif)
所以椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-59109.gif)
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-67657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180239-12070.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180239-31622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180239-73879.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180239-78511.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180240-82219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180240-83245.gif)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180240-35356.gif)
设线段
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180237-19402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180240-35008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180240-35008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180240-16376.gif)
由题意有
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180241-30403.gif)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180241-85989.gif)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180241-22059.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180241-50089.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180242-79203.gif)
(Ⅲ)设椭圆上焦点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180242-86921.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180242-38737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180242-10982.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180241-22059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180242-79986.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180243-96394.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180243-55758.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180243-97136.gif)
所以△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-69803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180243-15797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180243-12473.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180244-99133.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180244-73776.gif)
可知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180244-72276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180244-89323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180245-33915.gif)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180245-23801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180244-72276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180245-23477.gif)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180245-23801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180238-69803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180245-83025.gif)
解析
核心考点
试题【已知椭圆的离心率为,且两个焦点和短轴的一个端点是一个等腰三角形的顶点.斜率为的直线过椭圆的上焦点且与椭圆相交于,两点,线段的垂直平分线与轴相交于点.(Ⅰ)求椭圆】;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/20191023/20191023180212-91120.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-20851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-99425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-17072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-18742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-48232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-91120.gif)
(1)求证:在黄金椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-91120.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-20851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-99425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180214-22105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180214-97480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180214-45722.gif)
(2)黄金椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-91120.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-20851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-99425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180214-89228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-29859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-91120.gif)
任意一点.是否存在过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-82514.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-29859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-40162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-40162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-68328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180216-26726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180216-73456.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-40162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180216-34617.gif)
(3)在黄金椭圆中有真命题:已知黄金椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-91120.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180212-20851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180213-99425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180216-77849.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180214-89228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180217-33143.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180217-84920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180217-35480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180218-87016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180218-62060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180218-45785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180215-82514.gif)
设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180208-37355.gif)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180209-75006.gif)
(Ⅰ) 求椭圆E的方程;
(Ⅱ)已知过点M(1,0)的直线交椭圆E于C,D两点,若存在动点N,使得直线NC,NM,ND的斜率依次成等差数列,试确定点N的轨迹方程.
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180155-80573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180155-14441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180155-38765.jpg)
(1)求椭圆C的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180155-41008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180156-95935.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180156-67663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180156-76349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180156-16204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180148-25493.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180149-75448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180149-93741.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180149-48800.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180149-17829.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180150-85097.gif)
(1)求椭圆方程;
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180150-55916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180150-44163.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180150-49278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180143-61304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180143-34398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180143-35603.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180144-91467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180144-98546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180144-21024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180144-96307.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180145-97882.gif)
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