题目
题型:不详难度:来源:
已知抛物线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133834-42794.gif)
(1)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133834-35664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133835-87994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133835-46989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133834-35664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133835-51787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-97691.gif)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-31821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133835-87994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-55027.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-31821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-51978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133837-64845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133837-19665.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133837-32860.gif)
(2)△OCD的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133837-80629.gif)
解析
解:
(1)因为抛物线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133834-42794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133838-67833.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133834-35664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133835-46989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133838-42887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133838-14442.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133839-78987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133839-18255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133837-32860.gif)
(2) 由直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-31821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133835-87994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133836-55027.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133839-16868.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133839-58036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133840-36650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133840-46902.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133840-11267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133840-80553.gif)
∴△OCD的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133837-80629.gif)
核心考点
试题【(本题满分10分)已知抛物线方程为,(1)直线过抛物线的焦点,且垂直于轴,与抛物线交于两点,求的长度。(2)直线过抛物线的焦点,且倾斜角为,直线与抛物线相交于两】;主要考察你对抛物线的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133826-51808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133827-88711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133826-51808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133827-41427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133826-51808.gif)
A.![]() | B.3 | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133757-88925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133757-40113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133758-38370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133758-50355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133758-33601.png)
⑴若切线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133758-50355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133758-26465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133759-20090.png)
⑵求证:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133759-53098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133740-69699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133740-44587.gif)
1)求抛物线方程.
2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133740-69204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133740-86522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133741-51173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133740-86522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133707-67822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133708-92237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133708-77434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133708-40783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133654-65860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133654-96280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133654-65860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-58009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-64159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-90363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-72780.png)
(Ⅰ)求出以y轴为对称轴,过
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-64159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-65984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133655-90363.png)
(Ⅱ)过抛物线的焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133656-83644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133656-78571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133656-10614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133656-82200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133657-64926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133657-64926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025133657-67437.png)
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