题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-40312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-68507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-52036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-56332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-68507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-86917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-88715.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-45940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-86917.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-40312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-54126.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-87820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-28159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-93829.png)
解析
试题分析:(1)根据抛物线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-52036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-54711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-20004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-92248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-77485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-88964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-52036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-51989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-94791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-86917.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-57344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-43325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-43891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-92248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-66466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-30399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-86917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-94791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212744-88924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212744-90965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212744-41507.png)
(1)由题意知,焦点为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-54711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-20004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-92248.png)
由抛物线的定义知,
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-77485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-88964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-52036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212744-96299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212745-19032.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212745-15094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212745-60355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-94791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-87820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-28159.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-57344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-43325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-43891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-92248.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-66466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212743-30399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212745-49344.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212746-73601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212746-12392.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212739-86917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212746-95677.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212742-94791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212746-60519.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212747-10261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212747-84393.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212744-88924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212747-96459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212747-54387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212747-72213.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212748-24619.png)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-54711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212740-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212748-48217.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212749-26925.png)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212749-34623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212749-40466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212749-94410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212749-23588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212750-82455.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212750-89201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212750-70933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212750-25780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212750-33093.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212751-37399.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212751-46180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212750-89201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212751-22018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212751-28365.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212744-41507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212741-93829.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212731-11317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212731-57652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212732-14186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212731-11317.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212724-38056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212724-69977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212724-82286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212725-42995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212725-73136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212725-10965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212725-54356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212724-82286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212709-52189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-92959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-30357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-46744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-15994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-65986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-27551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212711-52033.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212711-17947.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212711-79267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212711-28465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-46744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212712-16856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212710-15994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212712-86020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212711-28465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212658-14511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212658-40755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212658-20975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212659-83067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212659-68255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212659-70654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212659-99149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212700-78734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212700-64157.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212648-42939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212648-66242.png)
(1)求椭圆C的标准方程;
(2)设F为椭圆C的左焦点,T为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212648-13264.png)
(i)证明:OT平分线段PQ(其中O为坐标原点);
(ii)当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025212649-37311.png)
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