题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002122-85273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002122-96370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002122-96421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002123-86914.png)
(1)求椭圆的方程;
(2)过抛物线上一点P,作抛物线的切线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002123-98335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002123-98335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002123-47240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002123-79173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002124-25503.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002124-95059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002124-20180.png)
解析
试题分析:(1)因为点F的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002125-53170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002125-80981.png)
从而有
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002125-62448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002124-95059.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002125-84115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002125-32862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002126-58612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002123-98335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002126-24406.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002126-26960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002127-97079.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002127-78211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002127-52493.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002127-85303.png)
从而有
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002127-98789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002128-69060.png)
则有
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002128-23941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002128-97277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002129-75677.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002129-32421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002129-25544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002124-20180.png)
点评:对于直线与圆锥曲线的综合问题,往往要联立方程,同时结合一元二次方程根与系数的关系进行求解;而对于最值问题,则可将该表达式用直线斜率k表示,然后根据题意将其进行化简结合表达式的形式选取最值的计算方式
核心考点
试题【已知点是F抛物线与椭圆的公共焦点,且椭圆的离心率为(1)求椭圆的方程;(2)过抛物线上一点P,作抛物线的切线,切点P在第一象限,如图,设切线与椭圆相交于不同的两】;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/20191026/20191026002119-33504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002119-83740.png)
A.直线 | B.圆 | C.椭圆 | D.双曲线 |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002107-43442.png)
C:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002107-94450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002107-92691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002107-45867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002107-32219.png)
(Ⅰ) 求椭圆C的方程;
(Ⅱ) 是否存在点M,使以PQ为直径的圆经过点F2,若存在,求出M点坐标,若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002100-15898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002100-18631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002055-71218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002055-60145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002055-57377.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-67937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-83188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-83188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-19354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-86729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002041-86341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002041-13534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002041-23668.png)
(1)求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-86729.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002041-30580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002042-15876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002042-59854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-86729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-19354.png)
(3)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002042-53016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002040-86729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002042-11949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002043-79015.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002043-38756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002043-76212.png)
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