题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022751-43535.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022751-58618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022752-97925.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022753-94891.png)
(1)求轨迹
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022751-58618.png)
(2)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022753-28215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022753-33928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022754-89850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022754-32301.png)
答案
由c=2,2a=2,∴b2=3.故轨迹S的方程为x2-
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022754-20920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022754-86337.png)
(2)当直线l的斜率存在时,设直线方程为y=k(x-2),P(x1,y1),Q(x2,y2),与双曲线方程联立消y得(k2-3)x2-4k2x+4k2+3=0. ……5分
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022755-72569.png)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022755-10363.jpg)
解析
核心考点
试题【已知,,点满足,记点的轨迹为,过点作直线与轨迹交于两点,过作直线的垂线、,垂足分别为,记。(1)求轨迹的方程;(2)设点,求证:当取最小值时,的面积为.】;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/20191026/20191026022745-87630.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-34807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-71437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-59263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-40156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-87108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-86136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-73755.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-54882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-87108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-21771.png)
(1) 求点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-87108.png)
(2) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022738-89492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022738-28129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022737-21771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022738-28129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022738-13038.png)
(3) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022738-43754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022738-70241.png)
(文)如图,|AB
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022729-16957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022729-29809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022729-29809.png)
段AC上,满足=.
(I)求点M的轨迹方程;
(II)若过B点且斜率为- 的直线与轨迹M交于点P,点Q(t,0)是x轴上任意一点,求当ΔBPQ为锐角三角形时t的取值范围。
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022729-34628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022714-31626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022714-59567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022714-42859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022714-27511.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)若直线l交y轴于点M,且
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022715-91421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022715-61748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022715-61748.png)
(Ⅲ)连接AE、BD,试探索当直线l的倾斜角变化时,直线AE与BD是否相交于定点?若是,请求出定点的坐标,并给予证明;否则,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022715-99436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022702-58729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022702-82477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022702-58729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022703-24302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022703-35308.png)
(I)求点M的轨迹C的方程;
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022703-61246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022703-24995.png)
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