解题方法
1 . 在平面直角坐标系
中,圆
的圆心坐标为
,过点
只能作一条圆
的切线,以坐标原点
为极点,
轴正半轴为极轴建立极坐标系.
(1)求圆
的极坐标方程;
(2)直线
和圆
相交于不同的两点
,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bd6f58663db80a04ed4fa9cd8d8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1a07619b083995cc59033a42070ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7832b52f828116e61e21486499ca96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
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2 . 已知抛物线
的焦点
到准线的距离为2,圆
与
轴相切,且圆心
与抛物线
的焦点重合.
(1)求抛物线
和圆
的方程;
(2)设
为圆
外一点,过点
作圆
的两条切线,分别交抛物线
于两个不同的点
和点
.且
,证明:点
在一条定曲线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcaad42bf2523650e7e52f6f83244b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4f69ea33f31123544adb144786c8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062aa1fe63adc386230d0c06c1479e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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13卷引用:广东省广州市2023届高三一模数学试题
广东省广州市2023届高三一模数学试题河北省衡水市第十三中学2023届高三上学期1月月考数学试题陕西省西安市西北工业大学附属中学2022-2023学年高三上学期1月期末理科数学试题 (已下线)专题8 解析几何 第4讲 圆锥曲线中的定点,定值,探究性问题(已下线)模块十二 解析几何-2广东实验中学2023届高三第三次阶段考试数学试题江苏省徐州市新沂市第三中学2023届高三下学期3月月考数学试题江苏省南通市海安高级中学2023届高三下学期一模数学试题(已下线)专题8-2 圆锥曲线综合大题归类(讲+练)-2(已下线)重难点突破13 切线与切点弦问题 (五大题型)(已下线)专题18 圆锥曲线高频压轴解答题(16大题型)(练习)福建省泉州第五中学2022-2023学年高二下学期第二次临考数学仿真模拟试题(B)(已下线) 第3章 圆锥曲线的方程单元测试能力卷-2023-2024学年高二数学上学期人教A版(2019)选择性必修第一册
解题方法
3 . 瑞士著名数学家欧拉在1765年得出定理:三角形的外心、重心、垂心位于同一直线上,这条直线被后人称为“欧拉线”.在平面直角坐标系中作
,点
,点
,圆
是“欧拉线”上一点,过
可作圆的两条线切,切点分别为
.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa90db29dc0badb8a25921f9710f6b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d31cd03879d5c69ff11d0923f1ee82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872003897fb6163e4c8c710e3dadd7bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba861d23cadbae8db64943c323c864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
A.![]() ![]() |
B.圆![]() ![]() ![]() |
C.四边形![]() |
D.直线![]() |
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4 . 如图所示,平面直角坐标系
中,四边形
满足
,
,
,若点
,
分别为椭圆
:
(
)的上、下顶点,点
在椭圆
上,点
不在椭圆
上,则椭圆
的焦距为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd99a6862833b220a7371852a3570bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2f21563f519fc8c47288b2b020e63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d0d12d0e06969e58f56899ea3cd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171b08c1122ed5d395dc72e9a8ee1390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/3630d768-f176-4123-8f79-2f6d1f90d5b0.png?resizew=137)
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5 . 数学中有很多形状优美,寓意美好的曲线,曲线
就是其中之一,则曲线
所围成的封闭图形的面积是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dbd61c93b622e75a72ba87a29f7107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
6 . 已知圆
的圆心坐标为
,且圆
与直线
相切,过点
的动直线
与圆
相交于M,
两点,直线
与直线
的交点为
.
(1)求圆C的标准方程;
(2)
是不是定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a345a7eb70e98a5b371f74d643a1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求圆C的标准方程;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a07d7455629b233a951c95af934289.png)
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解题方法
7 . 已知点A为双曲线
的右顶点,
在双曲线
上,
,
的内切圆为
.
(1)求曲线
和
的方程;
(2)已知
,过D作
的两条切线分别交
于
,
两点,证明:直线
与
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c324152eb62d144d4871879703a6f7da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000ae80efddd9b12c68f11232b20b896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae49789dbaa9ee4c6f3e02eba2bb472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f77cc97a6c8eb68777d76f1b9b6992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
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3卷引用:云南省云南师范大学附属中学2023届高考适应性月考卷(五)数学试题
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8 . 古希腊著名数学家阿波罗尼斯与欧几里得、阿基米德齐名,他发现:平面内到两个定点
的距离之比为定值
的点所形成的图形是圆.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.已知在平面直角坐标系
中,
,点
满足
,则点
所构成的曲线为
为阿氏圆.下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08f5d6f91366da27e9b96452bb04977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf1db3d608d81245f34a0d7b1aaab2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df5d30e4268a4b86a4e098e8cb57da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.曲线![]() ![]() | B.曲线![]() |
C.从点![]() ![]() | D.曲线![]() ![]() |
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2卷引用:重庆市育才中学校2023届高三上学期第二次月考(12月)数学试题
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解题方法
9 . 已知圆
与直线
交于
两点,点
为线段
的中点,
为坐标原点,直线
的斜率为
.
(1)求
的值及
的面积;
(2)若圆
与
轴交于
两点,点
是圆
上异于
的任意一点,直线
,分别交
于
两点.当点
变化时,以
为直径的圆是否过圆
内的一定点,若过定点,请求出定点;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ef640c5594af2bea46a322c5f671cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63414dc4bac8ce524634b84b43dd8fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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10 . 已知实数
满足
,
,
,则
的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b672aad8cac57acdc9654d95699c00c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb32baabe10eeabdb867e296ad63783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102c4b6b476f28460083508db8c54024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979df095c33a0d8edce5c1fab7cad04.png)
A.![]() | B.6 | C.![]() | D.12 |
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5卷引用:福建师范大学附属中学2023届高三上学期12月月考数学试题