题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161010-10626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161010-67400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161010-10626.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-85425.png)
解析
∴逆矩阵M-1是把坐标平面上的点的纵坐标缩短到
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-32409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-58998.png)
∴M-1=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-91158.png)
任意选取椭圆 x2+y2=1上的一点P(x0,y0),它在矩阵 M-1=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-91158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-91158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161011-52714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161012-97077.png)
x0="2x" ′0
y0="3y" ′0 .
又因为点P在椭圆 x2+y2=1上,所以9x0"2+16y0"2=1.
椭圆 x2+y2=1在M-1的作用下的新曲线的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023161012-63859.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160956-78584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160957-19905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160957-55549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160957-23824.png)
(1)求椭圆C的方程;
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160957-23549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-84819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-70553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160956-78584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-29304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-98669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160956-78584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-45737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-98669.png)
(3)在(2)的条件下,证明直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160959-54864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160958-29304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160939-19699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160939-26598.png)
(I)求椭圆的方程
(II)若过点M(2,0)的直线l与椭圆C交于不同两点A、B,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160939-71358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160940-70561.png)
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160921-88013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160922-34528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160922-63494.png)
椭圆的短半轴长为半径的圆与直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160922-30997.png)
⑴求椭圆C的方程;
⑵设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160923-63786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160923-50939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160923-43520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160921-88013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160923-41580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160924-43055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160921-88013.png)
于另一点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160924-42123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160924-43055.png)
⑶在⑵的条件下,证明直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160924-29874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160923-41580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160915-66994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160916-56316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160916-22142.png)
A.![]() | B.![]() ![]() | C.![]() | D.![]() ![]() |
①已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160907-18366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160907-49991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160907-24231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160907-34261.png)
②已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160908-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160908-74386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160908-26679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160908-86068.png)
③若过双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160909-55338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160909-70251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023160909-58624.png)
④根据气象记录,知道荆门和襄阳两地一年中雨天所占的概率分别为20%和18%,两地同时下雨的概率为12%,则荆门为雨天时,襄阳也为雨天的概率是60%.
其中正确命题的序号是( )
A.①③④ | B.①②③ | C.③④ | D.①②④ |
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