1 . 已知点S是圆
上任意一点,过S作x轴的垂线,垂足为H,点T满足
,记点T的轨迹为C.
(1)求轨迹C的方程;
(2)设轨迹C与x轴的交点分别为
,
,与y轴正半轴的交点为B,M是轨迹C上任意一点,且M不在坐标轴上.若直线
与直线
交于点P,直线
与直线
交于点Q.试判断
的形状,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13c02c5acb8df76da6356e504ded016.png)
(1)求轨迹C的方程;
(2)设轨迹C与x轴的交点分别为
![](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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
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解题方法
2 . 已知在
中,
.证明:
(1)
;
(2)
在
上恒成立;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a98e220a9a1f2a1caa37e4cf4e213.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5e4691210486a560c59df09937d9f8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a6e773c41687e5b13d36da7612e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb222ce13688da6fc57089ebf5812b0e.png)
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解题方法
3 . 如图,已知抛物线
,
为其准线.
为
上一动点,过点
作
于
,直线
交抛物线于点
.若直线
过定点
.
(1)求
的值;
(2)过抛物线
上一动点
作抛物线
的两条切线,切点为
、
.记
的外心为
.证明:以
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a9efe4c27ce894634c9e4c737b5fd7.png)
![](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/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb50782b4a4f59f8798a90086b0d5c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74973a2eb4281a6943a506b779740ca7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/2/c8b920e2-0711-4e77-866a-534d8d8da985.png?resizew=126)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b57041b43206fc0d477f8c769078f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d48de5a380ae57e1094720433ab1d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
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4 . 已知
,则下列说法正确的有______ .
①若
有且仅有一个零点,则
;
②若
有且仅有一个零点,则
;
③若
有且仅有两个零点,则
;
④若
有且仅有一个极值点
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33dfa2e69a4d9cf93797b1f95c0a8e.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db0eb7b60e88da1d807797cb17f85d0.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65f98fb31af1299a4d4b31d67a240b0.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe33a19334467abffbd1f79ab245ce4e.png)
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解题方法
5 . 若
在
恒成立,则k的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e39613f9c965aa2d981420ed31647f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-03-02更新
|
1294次组卷
|
3卷引用:四川省成都市锦江区嘉祥外国语高级中学2020-2021学年高二下学期期中考试理科数学试题
四川省成都市锦江区嘉祥外国语高级中学2020-2021学年高二下学期期中考试理科数学试题(已下线)导数专题:利用导数研究函数零点的4种常见考法-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)辽宁省沈阳市东北育才学校2022-2023学年高二下学期期中数学试题
6 . 如图,P为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0ac188b55d6377c0ab00a28f3b9296.png)
上的动点,过P作椭圆
的切线交圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780231ff0af68a65a3d740a2c858b26.png)
于M,N,过M,N作
切线交于Q,则Q的轨迹方程为_______________ ;
的最大值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0ac188b55d6377c0ab00a28f3b9296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6992d4a7cfa2348894f7c991ed6171c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780231ff0af68a65a3d740a2c858b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95f1a8e66ddfb0277c3efb15bf8b7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9902b08a6e0aef5eac29c197a356320b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/de5896a5-8ca6-48a2-8ae5-bc88e615bf8e.png?resizew=219)
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7 . 已知抛物线C:
(p>0),过C的焦点F的直线
与抛物线交于A、B两点,当
⊥x轴时,|AB|=4.
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842695095574528/2927812091486208/STEM/1f767413c15748769d872c2d4ae759f4.png?resizew=199)
(1)求抛物线C的方程;
(2)如图,过点F的另一条直线
与C交于M、N两点,设
,
的斜率分别为
,
,若
(
),且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842695095574528/2927812091486208/STEM/1f767413c15748769d872c2d4ae759f4.png?resizew=199)
(1)求抛物线C的方程;
(2)如图,过点F的另一条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06744e0406608a46242aa6c2b194870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eec363212db572fbb9046aee21b4f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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7卷引用:四川省凉山州2021届高三二模数学(文科)试题
解题方法
8 . 已知函数
的最大值为1.
(1)求常数
的值.
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d79136a8275adc65d8873f1d3684e7.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21abcd7a8febd3c2559320ac89de574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a415767156945ea8ada9ed3756019fc.png)
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9 . 已知函数
.若
有两个零点
、
.
(1)求
的取值范围;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4aa521eb592905bcac50c9e8e034c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e535a00f1c74f82ccac97f3fbacaa791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf096743ec9dc284c8463ef6b1aecdb.png)
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10 . 已知椭圆
的一个焦点为
,离心率为
,点P为圆
上任意一点,
为坐标原点.
(1)记线段OP与椭圆C的交点为Q,求
的取值范围;
(2)设直线l经过点P,且与椭圆C相切,与圆M相交于另一点A,点A关于原点的对称点为B,试判断直线PB与椭圆C的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b7ac31193004dcb7a71e8f657ad897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5f931d7a4bb4b9f7265f200248bac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)记线段OP与椭圆C的交点为Q,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b1113864968119e61aeee9ba9c613b.png)
(2)设直线l经过点P,且与椭圆C相切,与圆M相交于另一点A,点A关于原点的对称点为B,试判断直线PB与椭圆C的位置关系,并证明你的结论.
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