题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143035-19112.png)
(1)求椭圆C的方程;
(2)设直线l1的斜率k>0,在x轴上是否存在点P(m,0),使得以PG,PH为邻边的平行四边形为菱形?如果存在,求出m的取值范围;如果不存在,请说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-49616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-13400.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-96571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-97475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143035-19112.png)
所以椭圆C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-49616.png)
(2)由题意可知,直线l1的方程为y=kx+3(k>0).
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-63981.png)
Δ=(24k)2-4×24×(3+4k2)>0,解得k>
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143037-95120.png)
设椭圆的弦GH的中点为N(x0,y0),则“在x轴上是否存在点P(m,0),使得以PG,PH为邻边的平行四边形为菱形”等价于“在x轴上是否存在点P(m,0),使得PN⊥l1”.
设G(x1,y1),H(x2,y2),由韦达定理,得x1+x2=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143037-76412.png)
则x0=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143037-86658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143037-86262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143038-88440.png)
即N
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143038-62870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143038-67098.png)
从而-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143038-67098.png)
解得m=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143038-77876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143039-77555.png)
又因为m′(k)=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143039-43710.png)
所以函数m=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143038-77876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143039-97168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143039-90688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143039-36148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-13400.png)
故存在满足条件的点P(m,0),m的取值范围为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143036-13400.png)
核心考点
试题【在平面直角坐标系xOy中,椭圆C的中心为原点,焦点F1,F2在x轴上,离心率为.过F1的直线交椭圆C于A,B两点,且△ABF2的周长为8.过定点M(0,3)的直】;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/20191023/20191023143013-62457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143013-32818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143013-13430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143014-53369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143014-34941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143014-22920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143014-67407.png)
(1)求该椭圆的标准方程;
(2)当点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143014-83661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143013-62457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143015-88255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143015-21895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143015-40091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143015-46290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-61039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143015-21895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-22502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-89241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-20455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-43588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-90253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143016-43588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143002-81693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143002-14526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143003-52441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143003-32174.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143003-13582.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143002-14526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143003-16696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143003-10411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023143004-46954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142950-99216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142950-68550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142951-66576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142951-34088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142950-68550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142951-95636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142951-81449.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142941-63304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142941-22596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142941-68331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142942-13451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142942-80612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142942-90077.png)
(1)若命题
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142941-63304.png)
(2)若命题
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142941-63304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142942-13451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142942-46842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142924-56069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142924-50634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142924-70063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142924-13774.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142924-51866.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142925-37355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142924-51866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142925-36232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142925-79771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142925-76016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142926-89233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023142926-11551.png)
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