题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151036-46833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-53174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-89293.png)
(1)求椭圆的方程;
(2)若过点C(-1,0)且斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-45354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-33638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-33216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-90355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-28726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-25292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-57977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-28726.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-26524.png)
(2)在x轴上存在点M(
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-40038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-25292.png)
解析
试题分析:(1)∵椭圆离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-79239.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-28478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-51575.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-19966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-17884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-46879.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-91530.png)
∴椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-26524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-67116.png)
(2)在x轴上存在点M
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-42787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-25292.png)
证明:假设在x轴上存在点M(m,0),使
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-25292.png)
∵直线L过点C(-1,0)且斜率为K,∴L方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-26561.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-30119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-77248.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151039-99030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-32158.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-30535.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-59253.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-37148.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-79626.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-48678.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151040-73982.png)
设常数为t,则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151041-32800.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151041-37972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151041-19336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151041-56438.png)
即在x轴上存在点M(
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151038-40038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-25292.png)
点评:中档题,曲线关系问题,往往通过联立方程组,得到一元二次方程,运用韦达定理。求椭圆标准方程时,主要运用了椭圆的几何性质,建立了a,bac的方程组。(2)作为研究
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151037-25292.png)
核心考点
试题【已知椭圆的离心率为,且过点.(1)求椭圆的方程;(2)若过点C(-1,0)且斜率为的直线与椭圆相交于不同的两点,试问在轴上是否存在点,使是与无关的常数?若存在,】;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/20191023/20191023151022-10182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-89922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-48377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-89922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151024-67318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-85806.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
(2)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-80436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-15065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-37947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-38005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-15841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-91792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-15841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-62482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-15413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-62482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151015-45559.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-62482.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151015-11929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151015-68172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150959-34916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150959-54151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-92329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-78475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-97956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-56364.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-84962.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-94802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-94675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-31926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151002-30235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151002-84192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151002-56028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151003-94702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150948-31114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-75697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-88792.png)
(Ⅰ)求动点M的轨迹C的方程;
(Ⅱ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-44673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-35463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-44678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-89861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-57423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-73073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-67086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-20073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-57576.png)
(Ⅰ)求椭圆方程;
(Ⅱ) 直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-42929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-24773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-62441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-67414.png)
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