名校
解题方法
1 . 已知抛物线C的顶点为原点,焦点F在x轴的正半轴,F到直线
的距离为
.点
为此抛物线上的一点,
.
(1)求抛物线方程和N点坐标;
(2)已知A、B是抛物线C上的两个动点,且点A在第一象限,点B在第四象限,直线
分别过点A、B且与抛物线C相切,P为
的交点.设C、D为直线
与直线
的交点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7116071164cdc45f5d312a437c68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c9ca0f54b6a84bb93d435933aae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715426331815c4e34ad97a8b66ab3ddd.png)
(1)求抛物线方程和N点坐标;
(2)已知A、B是抛物线C上的两个动点,且点A在第一象限,点B在第四象限,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
名校
2 . 点列,就是将点的坐标按照一定关系进行排列.过曲线C:
上的点
作曲线C的切线
与曲线C交于
,过点
作曲线C的切线
与曲线C交于点
,依此类推,可得到点列:
,
,
,…,
,…,已知
.
(1)求数列
、
的通项公式;
(2)记点
到直线
(即直线
)的距离为
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec391f08f1452fb3e0aebe7e12ba4fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a4422395ca20fe847419ec569e48b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddbde5d269189fced4cc478908a6866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec391f08f1452fb3e0aebe7e12ba4fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a4422395ca20fe847419ec569e48b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddbde5d269189fced4cc478908a6866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9979465ce76b8582067703b39a0bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
(2)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f04dcabdafec74f98f4a1f4faa3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db2da4189bf5f95ae10e6b96ee4b72e.png)
您最近一年使用:0次
名校
解题方法
3 . “曼哈顿距离”是人脸识别中一种重要的测距方式.其定义为:如果在平面直角坐标系中,点
的坐标分别为
,那么称
为
两点间的曼哈顿距离.
(1)已知点
分别在直线
上,点
与点
的曼哈顿距离分别为
,求
和
的最小值;
(2)已知点
是曲线
上的动点,其中
,点
与点
的曼哈顿距离
记为
,求
的最大值.参考数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6037359d2727b05ee33db9e2c36226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c6d5bcaa69cea79b24688f5d1bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c37a37e91dd29058e66d8d905e5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00535516e08775f69df930f449f4469e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c37a37e91dd29058e66d8d905e5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77e22dd917201d812897e3b4d1c52ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edc218828907b5918bf9d755eb98ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a9be71b631f37d8a88bc7bd030aa79.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e18b23c806c5c76de3244b015911e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d25e70d37af93796965efc8d342185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad135b14c9dcd83eab6618d7694c7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c33d08de0e3d2643654f22543132491.png)
您最近一年使用:0次
4 . (1)求经过两条直线
和
的交点,并且垂直于直线
的直线方程;
(2)已知圆
的圆心在直线
上,圆
与直线
相切,且在直线
上截得的弦长为
,求圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227d4946b9dbfdc8bef33b42b6a82572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6c22d1d53d8f0ed30d5c8a9cf30b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d717a25a45873801c0e6c1cba9468cd.png)
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5428b040be21dcd503d350478c0a4773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
解题方法
5 . 已知等腰
的一个顶点
在直线
:
上,底边
的两端点坐标分别为
,
.
(1)求边
上的高
所在直线方程;
(2)求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d230c11741700260723b295ca90e873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c80eabaf101288433b3b9e92a4805a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
(1)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
6 . 已知直线l和圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6af86fad48a0dce7de33e2565ee47da.png)
(1)若直线l过点
,且在两坐标轴上的截距互为相反数,求直线l的方程;
(2)过点
引直线与圆C相切,切点为N,求线段MN的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6af86fad48a0dce7de33e2565ee47da.png)
(1)若直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de78b493bc2cc9696c584325c22ee7.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb8f8f39e1d3eea420b0de792d20f38.png)
您最近一年使用:0次
解题方法
7 . 已知圆心为C的圆经过
,
两点,且圆心C在直线
上.
(1)求圆C的标准方程;
(2)求与直线AB平行且与圆C相切的直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c918b7042bed26495b497cf74ffa59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb6fd712d967a36c027693a54f91470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ed55b98860ae6c0fbf3663f6b9fa8.png)
(1)求圆C的标准方程;
(2)求与直线AB平行且与圆C相切的直线的方程.
您最近一年使用:0次
8 . 已知点
,
,
,直线
与
轴交于点
.
(1)求点
的坐标;
(2)求
的外接圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109a293cef44f23e86e22c1a4cfcbbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03add3189e2b3984c68146d0d95a963e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
9 . 已知圆
过点
,且圆心
在直线
上.
(1)求圆
的方程;
(2)若从点
发出的光线经过
轴反射,反射光线
恰好平分圆
的圆周,求反射光线
的一般方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d801297de80b335b19999b692f65de83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8a82a007d596239d4778c7d540e7d4.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2a5c155717f3a59d7818b4bbdf44e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
23-24高二上·全国·单元测试
10 . 已知点
,________,从条件①、条件②、条件③中选择一个作为已知条件补充在横线处,并作答.条件①:点
关于直线
的对称点
的坐标为
;条件②:点
的坐标为
,直线
过点
且与直线
垂直;条件③点
的坐标为
,直线
过点
且与直线
平行.注:如果选择多个条件分别解答,按第一个解答计分.
(1)求直线
的方程;
(2)求直线
:
关于直线
的对称直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c664dcdcf88a834707b415061bed5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db701ed2d5950fb1f6f69e18a68d7e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db701ed2d5950fb1f6f69e18a68d7e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c6b37048fcaecafbe675149ade549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c5d258a3877968aa9e14c17d5d7f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c6b37048fcaecafbe675149ade549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18feaed4f3dd7698210ba302c81dca6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次