名校
1 . 已知实数x,y满足方程
.
(1)求
的值;
(2)设
与
是方程组
两组不同的解,其中
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1beb6812158ca2a3082bd13ca07578f0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1afbc87ccffbc98b9ab58df8c69bee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99307ab4373fbe72422ae5aa980db61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41039d45e37899d233232de3d802b105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccee8eb181dc117834582bc433eca559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab3cf6695638d5bcd26580174d7cbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
您最近一年使用:0次
2 . 如图,直线
与直线
之间的阴影区域(不含边界)记为
,其左半部分记为
,右半部分记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/5ea293b0-aa12-40f1-b1e6-802fd9973139.png?resizew=163)
(1)分别用不等式组表示
和
;
(2)若区域
中的动点
到
的距离之积等于
,求点
的轨迹
的方程;
(3)设不过原点
的直线
与(2)中的曲线
相交于
两点,且与
分别交于
两点.求证
的重心与
的重心重合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2f99fee759b608a8f448d99d221171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df7b3f985f80216134feed07422c9e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/5ea293b0-aa12-40f1-b1e6-802fd9973139.png?resizew=163)
(1)分别用不等式组表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
(2)若区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd180baa7212528480ce32f2fda8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)设不过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237c115d5b39d761e1cbcae031070b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10904093548255b8b1a7cb6ce712c240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2891d9f9d1843f129b96ccb6808e4bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2240b688ffb2cb0da2530940bd3aa4d1.png)
您最近一年使用:0次
2022-11-10更新
|
479次组卷
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2卷引用:2005年普通高等学校招生考试数学(文)试题(北京卷)