名校
解题方法
1 . 如图,已知圆
,
为直线
上一动点,
为坐标原点,过点
作圆
的两条切线,切点分别为
,
.
(1)证明直线
过定点,并求出定点的坐标;
(2)求线段
中点的轨迹方程;
(3)若两条切线
,
与
轴分别交于点
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8b74d61c82a73fd4dad8f122fe6fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aefcf9299f5c114ef8a072d3279d625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/2/50ba8f05-5f7d-46fc-866c-1279b3499757.png?resizew=164)
(1)证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)若两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a670d12554358604dc27abf2eaf1732.png)
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2023-10-14更新
|
693次组卷
|
2卷引用:四川省眉山市仁寿县仁寿第一中学校南校区2023-2024学年高二上学期期中数学试题
2 . 已知圆
,直线
.
(1)若圆O的弦AB恰好被点
平分,求弦AB所在直线的方程;
(2)点Q是直线l上的动点,过Q作圆O的两条切线,切点分别为C,D,求直线CD经过的定点;
(3)过点
作两条相异的直线,分别与圆O相交于E,F两点,当直线ME与直线MF的斜率互为倒数时,求证:线段EF的中点G在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393a0e30b023f2a20d366eef481b5eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41888144f7eb9ca029d624560530d82.png)
(1)若圆O的弦AB恰好被点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
(2)点Q是直线l上的动点,过Q作圆O的两条切线,切点分别为C,D,求直线CD经过的定点;
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
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2023-02-23更新
|
315次组卷
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2卷引用:四川省广元市2022-2023学年高二上学期期末数学(文科)试题
3 . 如图,椭圆
的左顶点
,点
都在椭圆上不与顶点重合且关于坐标原点
对称,其中点
在第一象限,线段
的中点是
,点
在
轴上的投影是
,直线
交椭圆C于另一交点
.直线
的斜率分别是
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/d3d1e34d-1b34-4e04-b1bb-389423c75a7e.png?resizew=189)
(1)求证:
是定值并求出该定值;
(2)求证:
;
(3)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bf37fb661ccc2fdd67407269708df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/d3d1e34d-1b34-4e04-b1bb-389423c75a7e.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe870e7477244aab08cc0fd8de24971.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17277a306d4d0a0a0cf293f87802cf66.png)
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2023-02-07更新
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3卷引用:四川省宜宾市叙州区第一中学校2023-2024学年高二上学期期末数学试题
解题方法
4 . 直线
,圆
.
(1)证明:直线
恒过定点
,并求出定点
的坐标;
(2)求直线
被圆
截得的最短弦长;
(3)设直线
与圆
交于
两点,当
的面积最大时,求直线
方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6071f02b52b68a6d676379a708c534f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cd84868c8bffa4461c47a1bfc0b856.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)设直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
5 . 已知椭圆
与双曲线
有相同的焦点
,
为椭圆上一点,
面积最大值为
.
(1)求椭圆
的方程;
(2)直线
与椭圆
相交于
两点,若
轴,垂足为
.求证:直线
的斜率
;
(3)
为椭圆
的右顶点,若过点
且斜率不为0的直线
交椭圆
于
两点,
为坐标原点.问:
轴上是否存在定点
,使得
恒成立.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/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd404346873e85e782f63107082d7d8.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b343d77ee4dced82ecc479206c42977d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbbc9c5353894f2c93c205c3ac04f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc47d7c132eb5e257c9f89ddc8106db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d1a8a5df71823996cb843f146b43ba.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb448b813339bad24b1acbd6e484b340.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06cee2345dd9520f6cb27183dee9b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2023-07-06更新
|
759次组卷
|
5卷引用:四川省遂宁市2022-2023学年高二下学期期末数学理科试题
名校
解题方法
6 . 已知双曲线的实轴长为4,离心率为
.过点
的直线l与双曲线C交于A,B两点.
(1)求双曲线C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a149da548c87b345e0672cd47c8a02bb.png)
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2023-10-19更新
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1222次组卷
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6卷引用:四川省眉山市仁寿县第一中学2023-2024学年高二上学期期末模拟考试数学试题
四川省眉山市仁寿县第一中学2023-2024学年高二上学期期末模拟考试数学试题江西省南昌市江西师范大学附属中学2024届高三上学期数学素养测试试题(已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员【练】(已下线)考点19 解析几何中的探索性问题 2024届高考数学考点总动员(已下线)专题25 双曲线的简单几何性质9种常见考法归类(2)(已下线)专题12 双曲线的几何性质8种常见考法归类(3)
名校
解题方法
7 . 已知直线l:
.
(1)证明:直线l恒过第二象限;
(2)若直线l交x轴的负半轴于点A,交y轴的正半轴于点B,O为坐标原点,设
的面积为S,求S的最小值及此时直线l的一般式方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4dd26b9c01cc69e2d94d2078d165ff4.png)
(1)证明:直线l恒过第二象限;
(2)若直线l交x轴的负半轴于点A,交y轴的正半轴于点B,O为坐标原点,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2023-10-14更新
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317次组卷
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3卷引用:四川省内江市第一中学2023-2024学年高二上学期期中数学试题
8 . 圆
,直线
.
(1)证明:不论
取什么实数,直线
与圆
相交;
(2)求直线
被圆
截得的线段的最短长度,并求此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1cd21b824fcf58c75911fb165306d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9e1b7f03521a134391da9b1fbe9e98.png)
(1)证明:不论
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求直线
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-09-10更新
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1079次组卷
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10卷引用:四川省德阳中学校2023-2024学年高二上学期10月月考数学试题
四川省德阳中学校2023-2024学年高二上学期10月月考数学试题人教A版 全能练习 必修2 第四章 本章能力测评(四)沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 12.2(1) 圆的标准方程江西省赣县第三中学2020-2021学年高二上学期期中适应性考试数学(文)试题第四章 第二节4.2直线、圆的位置关系沪教版(2020) 一轮复习 堂堂清 第七单元 7.5 直线与圆的位置关系辽宁省大连市第八中学2019-2020学年高二上学期10月月考数学试题新疆伊犁州华·伊高中联盟2023-2024学年高二上学期期中数学试题广西壮族自治区百色市平果市铝城中学2023-2024学年高二下学期开学考试数学试卷(已下线)专题2.2 直线与圆的位置关系(2个考点十二大题型)(3)
9 . 如图,在平面直角坐标系
中,直线
与x轴交于点A,过l右侧的点P作
,垂足为M,且
.
(1)求点P的轨迹C的方程;
(2)过点
的动直线
交轨迹C于S,T.证明:以线段
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdd3be8e58a9150e5b1e2a43988fd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee166bece50bbf1fc8a647b69472d39a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/6/23301f40-c6d0-4131-a8b3-f1d876d57099.png?resizew=154)
(1)求点P的轨迹C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
您最近一年使用:0次
名校
解题方法
10 . 已知椭圆
的右焦点为
,点M是椭圆C上异于左、右顶点
,
的任意一点,且直线
与直线
的斜率之积为
.
(1)求椭圆
的标准方程;
(2)若直线
与直线
相交于点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.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/bbe61d39d080872caa8973a70a3b4955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448eb7d301baa90fe59b05761830f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2fb94c54bbc6c851adbd6b60590bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6e899065e9c620eadc98ea8a5beb5f.png)
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