1 . 已知圆
:
,过圆
外一点
作圆
的切线,切点为
,
,直线
与直线
相交于点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.若点![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.![]() ![]() |
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2 . 在平面直角坐标系
中,设点
是椭圆
上一点,以M为圆心的一个半径
的圆,过原点作此圆的两条切线分别与椭圆C交于点P、Q.
(1)若直线
的斜率都存在,且分别记为
.求证:
为定值;
(2)探究
是否为定值,若是,则求出
的最大值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e643123a5f7a219e2a3f4270fe1dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8176754726d2194c890e80df1a1f1c3a.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139c0ae68e597571ba72ef727fa9222c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(2)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f6c5fd93aed88bec58002a20ea2e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bab77b1212086d7b16e288f73a09560.png)
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解题方法
3 . 如图,在平面直角坐标系
中,已知双曲线
:
的右焦点为
,左、右顶点分别为
,
,过
且斜率不为0的直线
与
的左、右两支分别交于
、
两点,与
的两条渐近线分别交于
、
两点(从左到右依次为
、
、
、
),记以
为直径的圆为圆
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/07d8fe6f-6f3b-42b6-ae79-d601cc849399.png?resizew=149)
(1)当
与圆
相切时,求
;
(2)求证:直线
与直线
的交点
在圆
内.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767187f446dedae821d58facd64aed6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5660be1b6e0d3d1cab756d6f8f5855.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/a0ed1ec316bc54c37c4286c208f55667.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/07d8fe6f-6f3b-42b6-ae79-d601cc849399.png?resizew=149)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca04f7af5df5606674310523b55f92.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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名校
解题方法
4 . 过点
的直线与圆
交于
两点,在线段
上取一点
使得
,则线段
的长可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad0c17ee2a84d4fc28affe35f7c28b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8eb8a2f500cc064512eca601d66d23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e3f5792be4c72623f3712cdb66b056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc578b8121b06920648eadcec1563b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
5 . 在平面直角坐标系
中,已知圆
,若正方形
的一边
为圆
的一条弦,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/8d15ca2ed3a635cc717b0a21509525b9.png)
A.![]() | B.![]() | C.![]() | D.5 |
您最近一年使用:0次
2024-01-29更新
|
798次组卷
|
7卷引用:江苏省扬州市2024届高三上学期期末检测数学试题
江苏省扬州市2024届高三上学期期末检测数学试题江苏省南京市金陵中学2024届高三上学期期末模拟数学试题河南省焦作市博爱县第一中学2024届高三下学期开学摸底考试数学试题(已下线)第1套 重组模拟卷(模块二 2月开学)(已下线)第三套 新高考新结构全真模拟3(艺体生)(已下线)【练】专题7 解三角形与其它知识的交汇问题(已下线)专题1 直线与圆的位置关系【讲】(压轴小题大全)
6 . 已知点
在圆
上,点
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2025bac7b08ec9f206cfce02bdd7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243e699ef05dc31d5f577bef2a22801e.png)
A.存在点![]() ![]() | B.![]() |
C.存在点![]() ![]() | D.![]() |
您最近一年使用:0次
2024-01-26更新
|
371次组卷
|
2卷引用:江苏省南通市2024届高三第一次调研测试数学试题
名校
解题方法
7 . 在
中,已知D为边BC上一点,
,
.若
的最大值为2,则常数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffc13c9e743e54896921893abf8b190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6b69806d0f60aa5ec964460abd7ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd172042ed396eb8ff692912613fb2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-24更新
|
1573次组卷
|
9卷引用:江苏省扬州市2023-2024学年高二上学期1月期末数学试题
江苏省扬州市2023-2024学年高二上学期1月期末数学试题江西省赣州市南康中学2024届高三“九省联考”考后模拟训练数学试题(一)(已下线)考点18 解三角形中的范围问题 --2024届高考数学考点总动员【练】(已下线)专题18 三角形中关于角的最值问题(已下线)专题2 图形分割 定理优先【练】(经典母题)2024届广东省新改革高三模拟高考预测卷一(九省联考题型)数学试卷(已下线)重难点7-1 圆的最值与范围问题(8题型+满分技巧+限时检测)(已下线)第14题 三角形中常遇求范围,活用定理转化与回归(优质好题一题多解)(已下线)压轴小题14 定角类解三角形问题
名校
8 . 已知曲线
,若
到直线
的最小距离为______ ;若直线
与曲线
恰有2个公共点,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342e17a0b90b9bb6e4f3e62347d103a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c966320d637cab491c67425ef1338966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd194cab5f3d1978edf295f779385a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 已知圆
经过
中的三点,且半径最大.
(1)求圆
的方程;
(2)过点
的直线与圆
交于
两点(
在
轴上方),在
轴上是否存在定点
,使得
轴平分
?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b66ec9bf41dcc5784431ed5630f5261.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5b6926cdb99eb58070b8720718f71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e8e435259ab192d798bb8bf7774cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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解题方法
10 . 已知椭圆
的右顶点和上顶点分别为
,
,
为线段
的中点,
为坐标原点,且
.
(1)求椭圆
的方程;
(2)已知圆
,
为圆
上任意一点,过点
作椭圆
的切线,交圆
于点
,若
与
斜率都存在,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecedff6b4fbf069f6fd02dc62b52a734.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/ac047e91852b91af639feec23a9598b2.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/1b3cb5a30442f26ff9821376646ca519.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56648a303009f944e1a9983c3f62c7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee89f7d493efc00cd703af6bc73f9ea9.png)
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