题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231102-89370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231102-17892.png)
(Ⅰ)求该椭圆的直角标方程;若椭圆上任一点坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231102-48110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231102-66765.png)
(Ⅱ)若椭圆的两条弦
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-49330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-79737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-32651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-77875.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-48226.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231104-72439.png)
解析
试题分析:将椭圆的极坐标方程转化为一般标准方程,再利用换元法求范围,利用参数方程代入,计算得到结果.
试题解析:(Ⅰ)该椭圆的直角标方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231104-77164.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231104-55584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231104-25841.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231105-20314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231104-72439.png)
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-32651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231105-55965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-77875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231105-41520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231105-32657.png)
则直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231103-32651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231106-58784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231106-13705.png)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231106-65087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231106-97655.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231107-37389.png)
同理
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231107-27851.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231107-46714.png)
核心考点
试题【极坐标系中椭圆C的方程为以极点为原点,极轴为轴非负半轴,建立平面直角坐标系,且两坐标系取相同的单位长度.(Ⅰ)求该椭圆的直角标方程;若椭圆上任一点坐标为,求的取】;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/20191025/20191025231049-91707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231050-58799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231050-11228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231050-56983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231050-61439.png)
(Ⅰ)求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231051-48326.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231051-88882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231051-27800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231051-36338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231052-39006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231052-85606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231052-16896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231052-85606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231052-16896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231052-85380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231053-54598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231053-48736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231053-10186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231053-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231054-52103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231054-72221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231054-71350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-22289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-64570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-47651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-48901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-47487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-30268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-48976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-80682.png)
(1)求椭圆的方程;
(2)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-61395.png)
(3)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-30753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-55184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-30544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-34454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-38156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-67767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-61395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231025-11897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231026-79891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231026-23882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231027-45275.png)
(1)求曲线C的直角坐标方程;
(2)设直线l与曲线C相交于A、B两点,当a变化时,求|AB|的最小值.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-89497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-13653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-89497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-15201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-13653.png)
(1)求曲线C的方程;
(2)若过点M
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-84309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-21563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-10180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-13318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231018-68940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231004-84408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231004-78775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-85644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-15960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-72225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-23905.png)
(1)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-72225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-70441.png)
(2)若过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-37336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-79790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-70441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-46887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231007-71387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231007-11365.png)
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