题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025003-62774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025004-81498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025004-12380.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
答案
解析
解答:解:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025003-62774.png)
设椭圆上两点A(x1,y1)、B(x2,y2)关于直线y=4x+m对称,AB中点为M(x0,y0),
则 3x12+4y12=12,①
3x22+4y22="12" ②
①-②得:3(x1+x2)(x1-x2)+4(y1+y2)(y1-y2)=0,即 3?2x0?(x1-x2)+4?2y0?(y1-y2)=0,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025005-38484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025005-99469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025006-66065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025006-38597.png)
∴y0=3x0,代入直线方程y=4x+m得x0=-m,y0=-3m;
因为(x0,y0)在椭圆内部,
∴3m2+4?(-3m)2<12,即3m2+36m2<12,解得-
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025006-33756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025006-33756.png)
故选B.
核心考点
举一反三
.本小题满分15分)
如图,已知椭圆E:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024952-98929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024952-75038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024952-84978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024952-17824.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024952-25179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-13896.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-35057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-65143.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-80717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-14830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-99265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-68606.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-68606.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-93553.gif)
(1)求椭圆E与双曲线G的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-80717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024953-14830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-42453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-12307.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-42453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024955-82603.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024954-12307.gif)
(3)是否存在常数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024955-83941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024955-27640.gif)
若存在,试求出
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024955-83941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024947-23382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024947-64168.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024937-89613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024937-23645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024937-38171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-49354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-32409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024937-38171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-58996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-66581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-32348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-81628.gif)
(I)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-88632.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-88088.gif)
(II)设圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-32631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-42182.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-32631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-88088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-54498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-32631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024938-32348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-32631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-12759.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024939-45384.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024924-44712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024924-11459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024925-99979.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024925-20933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024925-91143.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024925-99979.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024925-97184.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024926-93049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024926-92627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024926-61055.gif)
(I)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024926-11524.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-87370.gif)
(II)设圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-43050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-55368.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-43050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-45997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-87370.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-43050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-55368.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-43050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-87370.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-75690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024928-10246.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-43050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024926-92627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024927-43050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024928-39699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024928-94906.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024915-47838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026024915-24836.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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