题目
题型:不详难度:来源:
(本题满分14分)已知直角坐标平面内点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200703-28365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200703-53212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200703-17175.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-56868.gif)
(Ⅰ)试求点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-13162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
(Ⅱ)若斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-71661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-23495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-12828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-73633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-31278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-30558.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-46297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-15686.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200707-21596.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200707-13128.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200707-82668.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200707-76714.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200708-43821.gif)
由椭圆的定义知点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-13162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
其中
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200708-14777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200708-67896.gif)
所以,轨迹
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200707-13128.gif)
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-23495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200708-47606.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200709-90386.gif)
联立直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200709-47761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200709-99011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200709-94238.gif)
(1)代入(2)得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200710-74935.gif)
化简得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200710-30319.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200710-76316.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200710-70475.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200711-48685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200709-47761.gif)
由韦达定理得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200711-29528.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200711-77650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200711-95554.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200712-32691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200712-27801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200712-67215.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200712-46186.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200713-99702.gif)
核心考点
试题【(本题满分14分)已知直角坐标平面内点到点与点的距离之和为(Ⅰ)试求点的轨迹的方程;(Ⅱ)若斜率为的直线与轨迹交于、两点,点为轨迹上一点,记直线的斜率为,直线的】;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/20191023/20191023200654-85887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-41882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-11841.gif)
A.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
B.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
C.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
C.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200646-85696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200646-77733.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200647-21691.gif)
(I)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200647-96399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200647-70370.gif)
(II)设直线AD,CB的斜率分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200647-71048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200647-48870.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200648-14803.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200638-76911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200638-47360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200639-72310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200639-79468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200639-78821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200639-62030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200639-59629.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200633-73948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-43438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-73683.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-59414.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-55525.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-37177.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-49864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-51626.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-89909.gif)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-43438.gif)
(Ⅱ)设向量
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-98646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-97142.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-96624.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200624-43438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200625-94663.gif)
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