题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130852-97310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130852-92319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130852-10087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-60985.png)
(1)求椭圆C的方程;
(2)已知动直线y=k(x+1)与椭圆C相交于A,B两点.
①若线段AB中点的横坐标为-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-21058.png)
②已知点M(-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-52974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-47975.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-32703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-40011.png)
(2)①±
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-43486.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130852-97310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130852-92319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-62984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130852-10087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-21058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-60985.png)
解得a2=5,b2=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-63570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-32703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-40011.png)
(2)设A(x1,y1),B(x2,y2).
①将y=k(x+1)代入
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-32703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-40011.png)
得(1+3k2)x2+6k2x+3k2-5=0,
∴Δ=48k2+20>0,x1+x2=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-74978.png)
∵AB中点的横坐标为-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-21058.png)
∴-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-74978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130855-43486.png)
②由(1)知x1+x2=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-74978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-25420.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-52974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-47975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
=(x1+
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
=(x1+
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
=(1+k2)x1x2+(
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-30297.png)
=(1+k2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-25420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130854-90530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-74978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-30297.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-49513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130856-30297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130857-15267.png)
核心考点
试题【已知椭圆C:+=1(a>b>0)的离心率为,椭圆短轴的一个端点与两个焦点构成的三角形的面积为.(1)求椭圆C的方程;(2)已知动直线y=k(x+1)】;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/20191023/20191023130848-88227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130848-32531.png)
A.线段 B.圆 C.椭圆 D.双曲线
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130835-20077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130835-29754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130835-89805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130835-71419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130836-47407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130836-62538.png)
A.p2-m2 | B.p-m | C.m-p | D.m2-p2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130828-29401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130829-54756.png)
A.P点有两个 | B.P点有四个 |
C.P点不一定存在 | D.P点一定不存在 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130814-49119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023130814-29830.png)
A.3![]() | B.4![]() | C.6![]() | D.12![]() |
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