题目
题型:不详难度:来源:
设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-64257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-32259.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-49003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-64257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-32259.gif)
x | 3 | —2 | 4 | ![]() | ![]() |
y | ![]() | 0 | —4 | ![]() | -![]() |
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-68349.gif)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-64257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-16650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-93224.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-32259.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-20149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-69543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-77987.gif)
(2)存在这样的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-20149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-19039.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-57180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-11578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-55905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-44594.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-40453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-96600.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-47674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-29840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-54224.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-69543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-77987.gif)
(2)假设存在这样的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-20149.gif)
设其方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034649-67184.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034650-68357.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034650-34706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034650-37780.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034650-46627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034647-49003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034650-34904.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034651-35090.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034651-17986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034651-31239.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034651-89348.gif)
将①②代入(*)式,得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034652-40245.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034652-70243.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034652-85949.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-50588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034648-19039.gif)
核心考点
试题【(本题满分12分)设椭圆、抛物线的焦点均在轴上,的中心和的顶点均为原点,从每条曲线上至少取两个点,将其坐标记录于下表中:x3—24y0—4- (1)求的标准方程】;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/20191026/20191026034638-60627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034638-25785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034639-98956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034639-40588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034639-92214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034639-35592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034639-35592.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
已知双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034623-90149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034624-65065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034624-65065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034624-75089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034624-81945.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034624-58200.gif)
(I)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034624-65564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034625-17175.gif)
(II)若动点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034625-69497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034625-32296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034625-28396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034625-69497.gif)
设动点P到点A(-l,0)和B(1,0)的距离分别为d1和d2,
∠APB=2θ,且存在常数λ(0<λ<1=,使得d1d2 sin2θ=λ.
(1)证明:动点P的轨迹C为双曲线,并求出C的方程;
(2)过点B作直线交双曲线C的右支于M、N两
点,试确定λ的范围,使
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034609-27494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034609-79290.gif)
O为坐标原点.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034609-18937.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034601-40956.png)
(Ⅰ)求点A的横坐标a与点C的横坐标c的关系式;
(Ⅱ)设曲线G上点D的横坐标为a+2,求证:直线CD的斜率为定值.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034558-29032.gif)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034558-87859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034558-18766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034559-83613.gif)
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