题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-61815.png)
(1)求动点P的轨迹C的方程;
(2)过点D(1,0)的直线l交轨迹C于不同的两点M,N,△MON的面积是否存在最大值?若存在,求出△MON的面积的最大值及相应的直线方程;若不存在,请说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-84413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-19152.png)
解析
∵A(-2,0),B(2,0),直线AP与直线BP的斜率之积为-
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-61815.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220002-30481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-61815.png)
化简整理得P点的轨迹C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-84413.png)
(2)依题意可设直线l的方程为x=ny+1.
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220002-94903.png)
设M(x1,y1),N(x2,y2),则y1+y2=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220002-37809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220002-46716.png)
△MON的面积S=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220003-46476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220003-46476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220003-12353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220003-85141.png)
令t=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220004-66895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220004-84139.png)
∴当t=1时,3t+
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220004-84139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025220001-19152.png)
此时直线的方程为x=1.
核心考点
试题【在平面直角坐标系xOy中,O为坐标原点,A(-2,0),B(2,0),点P为动点,且直线AP与直线BP的斜率之积为-.(1)求动点P的轨迹C的方程;(2)过点D】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215949-29710.png)
(1)求双曲线C的方程;
(2)若以k(k≠0)为斜率的直线l与双曲线C相交于两个不同的点M, N,且线段MA的垂直平分线与两坐标轴围成的三角形的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215950-33502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215931-63614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215931-67617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215932-41185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215932-42873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215932-64019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215932-91189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215932-32515.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215933-87533.png)
(2)若椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215933-87533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215933-96174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215933-12518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215933-27045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215933-63667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215934-10735.png)
(3)如果直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215934-93865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215931-63614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215934-20475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215934-59803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215934-20475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215934-59803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215935-67245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215935-92564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-86497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-17621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-87435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-17764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-58826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-38216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-81121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-11523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-97240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-86497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-53793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-89567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215917-72458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215916-53793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-86497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215917-62321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215917-60570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215918-58072.jpg)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215915-86497.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215918-32787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215859-84257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215900-18396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215900-16212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215900-93683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-43870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-83356.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-98018.png)
(2)过椭圆右焦点F2斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-25639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-67540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-67421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215901-98018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215902-98969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215902-88786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215902-52597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215903-19201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215903-64522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215903-69278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215903-11795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215903-23588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215904-63357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215904-22020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215851-79587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215851-75068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215851-79587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215851-75068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215851-79813.jpg)
(1)求P点的坐标.
(2)能否使直线CD过椭圆C1的右焦点,若能,求出此时双曲线C2的离心率;若不能,请说明理由.
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