名校
1 . 波斯诗人奥马尔·海亚姆于十一世纪发现了一元三次方程
的几何求解方法.在直角坐标系
中,P,Q两点在x轴上,以
为直径的圆与抛物线C:
交于点
,
.已知
是方程
的一个解,则点P的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19db0a8b4c9108e50d1d1de215220139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071d4c1556de22088445f191a80b8a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776bee64c15a10647a81af32c6c1082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a032228f52b919700de88ab7a806840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b80ba68333c85361226405acf33d56.png)
您最近一年使用:0次
名校
2 . 已知双曲线
左右焦点分别为
,点
为右支上一动点,圆
与
的延长线、
的延长线和线段
都相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24164ee062fd8c86ad35d50bb37c0090.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f06cddf90c2b1256b42462a270fd1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da01a3abe1c9dc4e6283afa0dc1a0d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24164ee062fd8c86ad35d50bb37c0090.png)
您最近一年使用:0次
2024高二下·上海·专题练习
3 . 已知点
在圆
上运动,若对任意点
,在直线
上均存在两点
,
,使得
恒成立,则线段
长度的最小值是 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061af1c7a4480004221e253d813efe07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6755d03c30c4a3987bdaf50a9d86a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
真题
4 . 圆
的圆心与抛物线
的焦点
重合,
为两曲线的交点,则原点到直线
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2942dff583234d3a682316271e1e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
您最近一年使用:0次
7日内更新
|
2092次组卷
|
5卷引用:专题08平面解析几何
2024高三·全国·专题练习
5 . 将函数
的图象绕坐标原点逆时针旋转θ(θ为锐角),若所得曲线仍是一个函数的图象,则θ的范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c92fd16a9f45a25aa6a615ac9d050a.png)
您最近一年使用:0次
2024高三·全国·专题练习
6 . 已知
满足
,则函数
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416d5e42afc12ecde0820b68b45911e2.png)
您最近一年使用:0次
解题方法
7 . 已知点
为圆
上位于第一象限内的点,过点
作圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3507fafd1db352f09d29355459cbcecb.png)
的两条切线
,切点分别为
,直线
分别交
轴于
两点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096ff746dcbbf5b53237f8b14844ba05.png)
_______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098658ddd8826dc6637297e1e6c7acdc.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ad3b1a11a6f66323223c37693f5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3507fafd1db352f09d29355459cbcecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260c5c6b68ba79277669d76d097f3976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b3f3c6e7712b32b861739dc84b004c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096ff746dcbbf5b53237f8b14844ba05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098658ddd8826dc6637297e1e6c7acdc.png)
您最近一年使用:0次
名校
8 . 已知动圆M经过点
、
,P是圆M与圆C:
的一个公共点.当
最大时,圆
的半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee33736169c249a029f478a605dc2c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8128ddbc498393e3ea2475df1ab2f4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee045fcf052cb7562aeca2e86f6346f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
9 . 古希腊著名数学家阿波罗尼斯发现:若动点M与两个定点A,B的距离之比为常数
(
,
),则点M的轨迹是圆.后来,人们将这个圆以他的名字命名,称为阿波罗尼斯圆,简称阿氏圆.已知
,M是平面内一动点,且
,则点M的轨迹方程为________ .若点Р在圆
上,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1e68a8b84c7062f763dd06beef5383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28ad58f426c58a9b2b89be292191dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f817d5f7090558cffccf8c3cd82c0493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d183e00fa84e9df65c1e90d6b647c872.png)
您最近一年使用:0次
10 . 已知抛物线
与圆
相交于四个不同的点
,则r的取值范围为______ ,四边形
面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99622d39db9a625fb4c4e30f6547db4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次