题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123346-61033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123346-26480.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123346-57875.png)
解析
试题分析:利用抛物线的焦点坐标确定,双曲线中c的值,利用双曲线上的点到坐标原点的最短距离为1,确定a的值,从而可求双曲线的标准方程。解:抛物线y2=8x得出其焦点坐标(2,0),故双曲线的c=2,
∵双曲线上的点到坐标原点的最短距离为1,∴a=1,∴b2=c2-a2=3,∴双曲线的标准方程是
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123346-57875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123346-57875.png)
点评:本题考查抛物线的标准方程与性质,考查双曲线的标准方程,确定几何量是关键.
核心考点
举一反三
已知四点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123329-30718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123330-53326.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123330-38172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123330-88391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123331-22302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123331-97710.gif)
(Ⅰ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123331-69593.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123331-96671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123332-76892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123332-79930.gif)
(Ⅱ)当点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123331-22302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123332-43811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123331-97710.gif)
ⅰ)以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123332-51431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123333-92688.gif)
ⅱ)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123333-45327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123333-87971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123333-87971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123334-47452.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123333-45327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123334-52587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123333-87971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123334-54023.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123334-74891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123335-79203.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123311-43522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123311-74898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123311-95915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123312-82446.png)
(1)求抛物线方程;
(2)设动直线l与抛物线E相切于点P,与直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123312-66667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123256-27302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123256-33717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-27178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-83491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-22768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-90757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-27178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-90757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123256-27302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123258-88424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123258-86575.png)
(Ⅰ) 求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123256-27302.png)
(Ⅱ) 当点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123258-49302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-27178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123259-82259.png)
(Ⅲ) 当点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-90757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123257-27178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123259-14753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123232-99515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123233-18480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123233-85198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123233-98660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123234-40783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123234-72123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123234-74492.png)
(I)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123234-63015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123235-12103.png)
(II)若点M到直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123234-74492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123235-86486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123118-53752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123118-78787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123118-30994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123118-43138.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123119-10659.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123119-80280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123118-30994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123119-23956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123121-43414.jpg)
(1)用
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123121-64643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123122-38188.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123119-80280.gif)
(2)当实数
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123122-38188.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123122-31577.gif)
并求此时
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123122-68301.gif)
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