题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200743-62137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200743-73320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200743-91529.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-32717.gif)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-89227.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-67990.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-29828.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-27346.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-10579.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-45818.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-60310.gif)
椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-27346.gif)
(2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-88498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200746-49827.gif)
由于直线与椭圆有两个交点,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200746-39113.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200746-79232.gif)
解二:(1) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200746-17410.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200747-20592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200747-22073.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200747-85763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200747-39350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200748-35707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200748-43912.gif)
把②代入①得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200748-27798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200748-98094.gif)
由②得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-84831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-13698.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-29828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-79191.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-90884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200747-39350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200746-79232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-14656.gif)
故所求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-29828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-10579.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200746-17410.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-29828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-79191.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200749-90884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200744-29828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200745-10579.gif)
————10分
核心考点
试题【椭圆的中心在原点,焦点F在轴上,离心率为,点到F点的距离为,(1)求椭圆的方程;(2)直线与椭圆交于不同的两点M、N两点,若,求实数的取值范围。】;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
请阅读以下材料,然后解决问题:
①设椭圆的长半轴长为a,短半轴长为b,则椭圆的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200737-43184.gif)
②我们把由半椭圆C1:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200737-70021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200738-94163.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200738-44225.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200737-70021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200738-26441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200738-98833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200739-29921.gif)
如右上图,设点F0,F1,F2是相应椭圆的焦点,A1,A2和B1,B2是“果圆”与x,y轴的交点,若△F0 F1 F2是边长为1的等边三角形,则上述“果圆”的面积为 。
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200739-94174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200720-51217.gif)
如图,已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200720-98864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200720-53814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200720-15949.gif)
(1) 求经过
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200721-12501.gif)
(2) 过椭圆上的点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200721-29897.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200721-29897.gif)
椭圆的一焦点与短轴两顶点组成一个等边三角形,则椭圆的离心率为( )
A.![]() | B.![]() | C.![]() | D.![]() |
(本题满分14分)已知直角坐标平面内点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200703-28365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200703-53212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200703-17175.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-56868.gif)
(Ⅰ)试求点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-13162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
(Ⅱ)若斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-71661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-23495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-81900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-12828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200705-73633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200704-50151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-31278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-30558.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-46297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200706-15686.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200707-21596.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200654-85887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-41882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-11841.gif)
A.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
B.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
C.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
C.随着角度
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-17077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200655-77605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200656-26476.gif)
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