题目
题型:不详难度:来源:
已知椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184818-28593.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184818-60224.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184818-60233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-13644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-75810.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-20628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-20628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-19330.gif)
(1)求满足条件的椭圆方程和抛物线方程;
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-92216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-92216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-96481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-33273.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-13141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-33273.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-79956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-78968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-48111.gif)
(2) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-18799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-21802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-51743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-48577.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-60049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-75072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-75810.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-70770.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184824-50982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-75072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-96481.gif)
轴上的椭圆.
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184824-19462.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-75810.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184824-17198.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184824-55643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-20628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184825-64847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184825-71980.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-13644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184825-27560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184826-77751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184826-90574.gif)
∴抛物线在点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-20628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184826-77785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184827-37985.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184827-94218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184827-53596.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-19330.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184827-48614.gif)
又由椭圆方程及
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184818-60224.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184827-13548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-19330.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184828-45812.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184828-45096.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184828-36821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184828-48954.gif)
∴椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-78968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-48111.gif)
(2)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-92216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184829-58832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184829-16778.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-13141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184829-27922.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184829-96943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184829-25578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184830-39725.gif)
将其代入椭圆方程得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-75072.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-18799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-21802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-51743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184822-48577.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-60049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-75072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184819-75810.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-70770.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184824-50982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184821-23736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184823-75072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184820-96481.gif)
轴上的椭圆. …………………………14分
核心考点
试题【(本小题满分14分)已知椭圆方程为(),抛物线方程为.过抛物线的焦点作轴的垂线,与抛物线在第一象限的交点为,抛物线在点处的切线经过椭圆的右焦点. (1)求满足条】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184812-21505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184812-20282.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184813-46238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184813-97876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184813-48129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184813-26210.gif)
(Ⅱ)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184813-70607.gif)
已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184756-37913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184756-90572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184756-75260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184757-21926.gif)
(1)求曲线E的方程;
(2)过点Q(1,0)且斜率为k的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184757-17759.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184757-72554.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184757-46063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184757-94413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184751-53685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184751-71740.gif)
|
|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184751-36736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184752-54669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184752-12735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184752-29761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184752-30357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184745-44389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184745-46428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184745-14660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184745-55385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023184740-57783.gif)
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