题目
题型:模拟题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122255-11285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122255-16830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122255-17669.png)
(1)求椭圆T的方程;
(2)是否存在斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122256-70130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122256-32104.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122256-24481.png)
设另一条切线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122256-39509.png)
则:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122256-57481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122257-29016.png)
此时切线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122257-36706.png)
切线方程与圆方程联立得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122257-44113.png)
则直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122257-89006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122257-62544.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122258-98450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122258-18263.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122258-86650.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122258-71268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122259-53767.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122259-92105.png)
故所求椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122259-46095.png)
(2)设存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122259-63572.png)
满足题意,联立
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122259-41942.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122300-29648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122300-92641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122300-78241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122300-68884.png)
则∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122301-30131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122301-53993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122301-62302.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122301-97591.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122301-56338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122302-63588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122302-14422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122302-64007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122303-33718.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122303-36526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122303-78489.png)
因此不存在直线满足题意。
核心考点
试题【已知圆C的方程为,过点作圆C的两条切线,切点分别为A、B,直线AB恰好经过椭圆的右顶点和上顶点。(1)求椭圆T的方程;(2)是否存在斜率为的直线l与曲线T交于P】;主要考察你对椭圆等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122242-73130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122242-36353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122243-31614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122243-70398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122243-11216.png)
(2)在(1)的条件下,过右焦点F2作斜率为k的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122243-94071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122229-55844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122229-60400.png)
B(0,b),且△ABF的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122229-90903.png)
(Ⅰ)求椭圆E的方程;
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122229-43180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122229-78734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122230-12605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122230-83339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122220-49878.png)
(1)求抛物线C1和椭圆C2的标准方程;
(2)过点F的直线交抛物线C1于A、B两不同点,交y轴于点N,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122220-60148.png)
(3)直线l交椭圆C2于P、Q两不同点,P、Q在x轴的射影分别为P"、Q",
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122220-37209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122220-99588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122214-62495.png)
(Ⅰ)求椭圆C1的方程;
(Ⅱ)设M(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122214-97514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122214-91958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122208-36391.png)
(Ⅰ)求椭圆C1的方程;
(Ⅱ)设M(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122208-24355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122208-58873.png)
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