题目
题型:不详难度:来源:
(文)已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012732-31041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012733-13951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012733-36671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012733-50721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012733-34999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012734-50698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012734-52914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012734-86779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012734-34500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-77215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-15687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-77215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-45476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-15687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-45476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-62711.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012733-50721.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-39799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-27030.png)
(3)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-44079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-77215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012735-45476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-30843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-75164.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012737-95597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012737-60438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-30843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-75164.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012737-37954.png)
解得a2=2,b2=1,
所以,椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012737-95597.png)
(2)设PQ:y=x-1,
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012737-17283.png)
解得: P(
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012738-81904.png)
由条件可知点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012738-45259.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012738-67862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012738-91548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012737-60438.png)
(3) 判断:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-30843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-75164.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012738-57312.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-44079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-30843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012739-11592.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012739-48115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012739-43865.png)
(x2-x1)y2-(x2-2)(y1+y2)=(x2-x1)k(x2-1)-(x2-2)(kx1-k+kx2-k)
=3k(x1+x2)-2kx1x2-4k=3k
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012739-96540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012739-69157.png)
=k(
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012740-47816.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-30843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012736-75164.png)
点评:高考中圆锥曲线的题目一般难度较大,而且一般运算量较大,要仔细运算,更要结合图形数形结合简化求解过程.
核心考点
试题【(本题满分16分) 本题共有3个小题,第1小题满分4分,第2小题满分6分. 第3小题满分6分.(文)已知椭圆的一个焦点为,点在椭圆上,点满足(其中为坐标原点),】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-80551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-55720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-42030.png)
给出如下定义:若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-17840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-33906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-74587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-19858.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-72733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-33906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012727-74587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012728-22991.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012728-54196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012728-91983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012728-50418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012728-54196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012728-50418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-18311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-54848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-54848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-18311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-43495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-18311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-54848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-18311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-54848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-21585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-12961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012719-30653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012719-61624.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-43495.png)
(2)某日,研究人员在
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-18311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-54848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-18311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012718-54848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012719-52990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012719-47125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012719-52990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012719-52990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012707-51671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012707-97738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012707-54043.png)
(1)求圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012707-51671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012708-37061.png)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012708-41909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012708-79416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012708-37061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012708-51423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012709-30066.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012709-71064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012708-41909.png)
②若点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012709-52645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012709-78879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012709-43764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012703-12529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012703-19712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012703-99371.png)
(理)已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012654-65921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012654-82001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012654-81203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012654-85464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012654-56824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-85297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-40475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-24047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-75456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-66237.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012654-85464.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-82446.png)
(3)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-25850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012655-75456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012656-58651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012656-60482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026012656-91356.png)
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