题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220543-24271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220543-63491.jpg)
(1)求椭圆C1的方程;
(2)求△ABD面积取最大值时直线l1的方程.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220543-54499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220544-54283.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220544-78242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220543-54499.png)
(2)设A(x1,y1),B(x2,y2),D(x0,y0).
由题意知直线l1的斜率存在,不妨设其为k,
则直线l1的方程为y=kx-1.又圆C2:x2+y2=4,
故点O到直线l1的距离d=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220544-29314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220544-82144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220545-91707.png)
又l2⊥l1,故直线l2的方程为x+ky+k=0.由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220545-73710.png)
消去y,整理得(4+k2)x2+8kx=0,
故x0=-
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220545-40638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220545-53863.png)
设△ABD的面积为S,则S=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220546-14993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220546-73984.png)
所以S=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220546-35494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220546-59728.png)
当且仅当k=±
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220544-54283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220544-54283.png)
核心考点
试题【如图,点P(0,-1)是椭圆C1:=1(a>b>0)的一个顶点,C1的长轴是圆C2:x2+y2=4的直径.l1,l2是过点P且互相垂直的两条直线,其】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
(1)求椭圆的方程;
(2)过F2的直线l与椭圆交于不同的两点M,N,则△F1MN的内切圆的面积是否存在最大值?若存在,求出这个最大值及此时的直线方程;若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220529-58755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220529-99392.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220511-14712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220511-88063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-51673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-33003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-35850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-33003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-80241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-19501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220513-75259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220513-70630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220513-73918.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-33003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-80241.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-80241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-19501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220514-28499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220514-93018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220512-33003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220514-40258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220514-62378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220514-28499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220515-69957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220515-51729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220505-32745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220505-85799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220505-32745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220506-93367.png)
条件 | 方程 |
①![]() | ![]() |
②![]() | ![]() |
③![]() ![]() | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220506-93367.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-88552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-91006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-95453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-95453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-91006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-88552.png)
C.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-91006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-88552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-95453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-88552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-95453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220507-91006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220451-98910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220452-34684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220452-20677.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220452-92235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220452-32200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220452-92235.png)
(2)设过定点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220453-52341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220453-36899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220453-47329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220453-84248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220454-33429.png)
中
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220454-28581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220453-36899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220454-40655.png)
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